Mathematical Sciences Research Institute - Introductory Workshop in Nonlinear Dispersive Equations

The field of nonlinear dispersive equations has experienced a dramatic growth in recent years, and continues to evolve at a rapid pace. For the most part the problems which are being considered have their origin in physics in subjects such as general relativity, quantum mechanics, water waves, nonlinear elasticity, various field theories, etc. There is also a significant component which is tied to geometry. Even though most of the research so far is mostly theoretical, there is also a strong potential for applications as one moves from model problems towards the original equations.

The key concept at the heart of the field is that of nonlinear wave interactions. These occur when waves, moving possibly with different speeds and in different directions, intersect. While in the linear theory such waves obey the principle of superposition, in nonlinear equations there is always some interaction. Initial research was concerned with interactions of small amplitude waves, which leads to small perturbations of linear regimes. However if the interaction is strong enough then it may create new waves or even lead to blow-up.

The aim of the workshop is to provide an overview of the problems and methods in the field, and also to survey some of the recent developments. We plan to have two or three series of expository talks given by mathematicians who are leaders in the field, and to complement this with a number of more specialized one hour talks in targeted areas.

Schedule

Monday, Aug 22, 2005

9:00-9:15 MSRI Welcome
9:15-10:15 Wilhelm Schlag I
10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations I"
Lunch Break
2:00-3:00 Jean Bourgain, "Normal forms in NLS"
3:30-4:30 Gustavo Ponce

Tuesday, Aug 23, 2005

9:15-10:15 Wilhelm Schlag II
10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations II"
Lunch
2:00-3:00 Kenji Nakanishi
3:30-4:30 Joachim Krieger, "Non-generic blow up solutions for the critical focusing NLS in 1-d"

Wednesday, Aug 24, 2005

9:15-10:15 Claude Zuily, "Strichartz estimates for the Schrodinger equation with variable coefficients"
10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations III"
Lunch
2:00-3:00 Ioan Bejenaru
3:30-4:30 Michael Christ, "Existence and nonuniqueness for the nonlinear Schrodinger equation"

Thursday, Aug 25, 2005

9:15-10:15 Jean-Yves Chemin, "Dispersive effects in high rotating fluids"
10:45-11:45 Wilhelm Schlag III
Lunch
2:00-3:00 Justin Holmer

Friday, Aug 26, 2005

9:15-10:15 Yoshio Tsutsumi, "Well-posedness of the Cauchy problem for the mKdV equation"
10:45-11:45 Jeremy Szeftel, "Long-time existence for semilinear Klein-Gordon equations on compact manifolds"

Currently Available Videos

Wilhelm Schlag , Nonlinear Dispersive Equations-Lecture I August 22,2005, 09:15 AM to 10:15 AM
Hart Smith , Wave Packet Methods for Hyperbolic Equations I August 22,2005, 10:45 AM to 11:45 AM
Jean Bourgain , Normal Forms in NLS August 22,2005, 02:00 PM to 03:00 PM
Gustavo Ponce , Nonlinear Dispersive Equations-Talk August 22,2005, 03:30 PM to 04:30 PM
Wilhelm Schlag , Nonlinear Dispersive Equations-Lecture II August 23,2005, 09:15 AM to 10:15 AM
Hart Smith , Wave Packet Methods for Hyperbolic Equations II August 23,2005, 10:45 AM to 11:45 AM
Kenji Nakanishi , Nonlinear Dispersive Equations-Talk August 23,2005, 02:00 PM to 03:00 PM
Joachim Krieger , Non-Generic Blow Up Solutions for the Critical Focusing NLS in1-d August 23,2005, 03:30 PM to 04:30 PM
Claude Zuily , Strichartz Estimates for the Schrodinger Equation with Variable Coefficients August 24,2005, 09:15 AM to 10:15 AM
Hart Smith , Wave Packet Methods for Hyperbolic Equations III August 24,2005, 10:45 AM to 11:45 AM
Ioan Bejenaru , Nonlinear Dispersive Equations-Talk August 24,2005, 02:00 PM to 03:00 PM
Michael Christ , Existence and Nonuniqueness for the Nonlinear Schrodinger Equation August 24,2005, 03:30 PM to 04:30 PM
Jean-Yves Chemin , Dispersive Effects in High Rotating Fluids August 25,2005, 09:15 AM to 10:15 AM
Wilhelm Schlag , Nonlinear Dispersive Equations-Lecture III August 25,2005, 10:45 AM to 11:45 AM
Justin Holmer , Nonlinear Dispersive Equations-Talk August 25,2005, 02:00 PM to 03:00 PM
Yoshio Tsutsumi , Well-Posedness of the Cauchy Problem for the mKdv Equation August 26,2005, 09:15 AM to 10:15 AM
Jeremie Szeftel , Long-Time Existence for Semilinear Klein-Gordon Equations on Compact Manifolds August 26,2005, 10:45 AM to 11:45 AM

You can find videos of other workshops and events on our VMath - Streaming Video page.

For more information:
Questions about this workshop should be sent either by email to

300@msri.org

or by regular mail to:

Introductory Workshop in Nonlinear Dispersive Equations Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

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