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Upcoming Colloquia & Seminars

  1. Applied fluids: Fluid-structure interaction involving incompressible, viscous fluids

    Location: MSRI: Online/Virtual
    Speakers: Suncica Canic (University of California, Berkeley)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract: In this talk we present some recent developments and open problems in the mathematical theory of nonlinear moving boundary problems describing the interaction between viscous, incompressible fluids, and elastic or poroelastic structures. Applications of the mathematical results to coronary angioplasty with stenting, and to bioartificial pancreas design will also be shown.

     

    Updated on Feb 09, 2021 06:16 AM PST
  2. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Feb 17, 2021 12:34 PM PST
  3. Career Development Seminar: How to have successful collaborations

    Location: MSRI: Online/Virtual
    Speakers: Charles Doering (University of Michigan), Juhi Jang (University of Southern California), Anna Mazzucato (Pennsylvania State University), Sung-Jin Oh (University of California, Berkeley), Daniel Tataru (University of California, Berkeley)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Updated on Feb 18, 2021 07:18 AM PST
  4. Model problems in fluid dynamics: Global well-posedness for the derivative nonlinear Schrödinger equation

    Location: MSRI: Online/Virtual
    Speakers: Galina Perelman (University Paris Est Creteil)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract.

    We consider the derivative nonlinear Schrödinger equation on the real line and show that the corresponding Cauchy problem is globally well posed for initial data in H^{1/2}.

    This is a joint work with Hajer Bahouri.

    Updated on Feb 24, 2021 07:28 AM PST
  5. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Feb 23, 2021 09:17 AM PST
  6. Water waves and other interface problems (Part 1): Angled crested like water waves

    Location: MSRI: Online/Virtual
    Speakers: Siddhant Agrawal (University of Massachusetts Amherst)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract

    In this talk, I will discuss angled crested like waves for the 2D water wave equation. I will first go over the a priori estimate of Kinsey and Wu (18) for angled crested water waves in the absence of surface tension. Then I will talk about rigidity results for such waves and in particular the behaviour of the angle of the corners. Finally I will talk about what one can say in the presence of surface tension. 

    Updated on Feb 25, 2021 06:18 AM PST
  7. Water waves and other interface problems (Part 2): The relativistic Euler equations with a physical vacuum boundary

    Location: MSRI: Online/Virtual
    Speakers: MARCELO DISCONZI (Vanderbilt University)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract:

    We consider the relativistic Euler equations with a physical vacuum boundary and an equation of state $p(\varrho)=\varrho^\gamma$, $\gamma > 1$. We establish the following results. (i) local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and continuous dependence on the data; (ii) low regularity solutions: our uniqueness result holds at the level of Lipschitz velocity and density, while our rough solutions, obtained as unique limits of smooth solutions, have regularity only a half derivative above scaling; (iii) stability: our uniqueness in fact follows from a more general result, namely, we show that a certain nonlinear functional that tracks the distance between two solutions (in part by measuring the distance between their respective boundaries) is propagated by the flow; (iv) we establish sharp, essentially scale invariant energy estimates for solutions; (v) we establish a sharp continuation criterion, at the level of scaling, showing that solutions can be continued as long as the velocity is in $L^1_t Lip_x$ and a suitable weighted version of the density is at the same regularity level. This is joint work with Mihaela Ifrim and Daniel Tataru.

    Updated on Feb 25, 2021 06:19 AM PST
  8. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Feb 23, 2021 09:18 AM PST
  9. Graduate Student Working Group: A stochastic fluid-structure interaction model given by a stochastic viscous wave equation

    Location: MSRI: Online/Virtual
    Speakers: Jeffrey Kuan (Harvard University)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract: We consider a stochastic fluid-structure interaction model, given by a stochastic viscous wave equation perturbed by spacetime white noise. This stochastic model is motivated by various applications in which one observes random deviations in real-life data. We prove that this stochastic viscous wave equation has a mild solution in dimension one, and also in dimension two, which is the physical dimension. This behavior contrasts that of the stochastic heat and wave equations, which do not have function valued mild solutions in dimensions two and higher.
    We also consider Hölder continuity path properties of solutions and show that the solution is Hölder continuous up to Hölder exponent 1/2 in both space and time, after stochastic modification. This is joint work with Suncica Canic.

    Updated on Feb 24, 2021 07:36 AM PST
  10. Euler/Navier Stokes (Part 1): Long time confinement of vorticity around stationary points for 2D perfect incompressible flows

    Location: MSRI: Online/Virtual
    Speakers: Dragos Iftimie (Université Claude-Bernard (Lyon I))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract:

    I will consider the 2D incompressible Euler equation in a simply-connected bounded domain. Such domains admit stationary points with the following property: a single point vortex located at that position will not move. In this talk I will discuss the problem of the long time confinement of the vorticity around such a stationary point. This is joint work with Martin Donati.

    Updated on Feb 25, 2021 08:06 AM PST
  11. Euler/Navier Stokes (Part 2): Geometric Structure of Mass Concentration Sets in Pressureless Euler Alignment Systems

    Location: MSRI: Online/Virtual
    Speakers: Trevor Leslie (University of Wisconsin-Madison)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract:

    In this talk, we will discuss the regularity theory and long-time behavior of solutions to the Euler Alignment model, focusing on the properties of the limiting density profile, which is in general a measure.  We show that for unidirectional data, the geometric structure of the singular support of this measure, i.e., the "mass concentration" set, can be understood almost completely in terms of the initial data.  

     

    Updated on Feb 25, 2021 06:30 AM PST
  12. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:32 PM PST
  13. Applied fluids: Confounding Complexities in Rayleigh-Bénard Convection

    Location: MSRI: Online/Virtual
    Speakers: Charles Doering (University of Michigan)

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

    Abstract: 

    Convection is buoyancy-driven flow resulting from unstable density stratification in the presence of a gravitational field.  Beyond its central role in myriad engineering heat transfer applications, convection underlies many of nature’s dynamical designs on larger-than-human scales. Indeed, solar heating of Earth’s surface generates buoyancy forces that cause the winds to blow, which in turn drive the oceans’ flow.  Convection in Earth’s mantle on geological timescales makes the continents drift, and thermal and compositional density differences induce buoyancy forces that drive a dynamo in Earth’s liquid metal core—the dynamo that generates the magnetic field protecting us from solar wind that would otherwise extinguish life as we know it on the surface.  The structure of the Sun itself relies on convection in the outer layers to transfer heat from the interior to radiate away from the surface.

    The key feature of convection is transport: thermal convection actively transports the heat that generates the density variations that produce the buoyancy forces.  Determining the rate at which “heat rises” in turbulent convection is one of the most important open problems in fluid dynamics.  In this presentation the confounding question of asymptotically high Rayleigh number heat transport in Rayleigh-Bénard convection – the buoyancy-driven flow in a horizontal layer of fluid heated from below modeled by the Boussinesq approximation to the Navier-Stokes equations – is reviewed from viewpoints of theory (models of the model), computation (direct numerical simulations), experiment (laboratory tests), and mathematical analysis (theorems).

     

    Updated on Feb 17, 2021 08:44 AM PST
  14. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Feb 23, 2021 09:18 AM PST
  15. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:02 PM PST
  16. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:02 PM PST
  17. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:34 PM PST
  18. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:02 PM PST
  19. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:02 PM PST
  20. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:03 PM PST
  21. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:34 PM PST
  22. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:04 PM PST
  23. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:35 PM PST
  24. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:05 PM PST
  25. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:05 PM PST
  26. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:35 PM PST
  27. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:05 PM PST
  28. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:12 PM PST
  29. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:12 PM PST
  30. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:35 PM PST
  31. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:13 PM PST
  32. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:13 PM PST
  33. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:14 PM PST
  34. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:36 PM PST
  35. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:14 PM PST
  36. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:14 PM PST
  37. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:17 PM PST
  38. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:36 PM PST
  39. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:18 PM PST
  40. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:20 PM PST
  41. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:20 PM PST
  42. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:36 PM PST
  43. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 27, 2021 02:20 PM PST
  44. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  45. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  46. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:36 PM PST
  47. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  48. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  49. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  50. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:36 PM PST
  51. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  52. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  53. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  54. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:37 PM PST
  55. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  56. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  57. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
  58. Fellowship of the Ring, National Seminar:

    Location: MSRI: Online/Virtual

    To attend this seminar, you must register in advance, by clicking HERE.

    Updated on Jan 11, 2021 04:37 PM PST
  59. Free surface flows in fluid dynamics (UCB Chancellor Professor Course)

    Location: MSRI: Online/Virtual
    Speakers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))

    To participate in this seminar, please register here: https://www.msri.org/seminars/25657

     

    A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

    These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

    Updated on Jan 28, 2021 01:33 PM PST
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