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.

Tea for members and participants.

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

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.

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

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.

Tea for members and participants.

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

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.

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. 

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.

Tea for members and participants.

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

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.

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

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.

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.  

Tea for members and participants.

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

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

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).

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

Tea for members and participants.

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

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.

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

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

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

Tea for members and participants.

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

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

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

Tea for members and participants.

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

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.

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