November 29, 2023

Thematic Program in Partial Differential Equations

March 15-19, 2004
Workshop on Nonlinear Wave Equations

Organizing Committee:
C. Bardos, J. Colliander, W. Craig (Chair), N. Ercolani, C. Sulem

Subject matter: Nonlinear microlocal analysis of evolution equations, the Boltzmann equation, kinetic equations (in general), statistical properties of Hamiltonian PDE

Abstract: There are numerous nonlinear evolution equations that have been derived in a context relevant to mathematical physics, for which it is a challenging mathematical problem to analyze the properties of the solution map for time evolution of the system. This workshop will focus on recent results on precise properties of solutions of the initial value problem, involving new techniques of harmonic and microlocal analysis for this purpose.

Principal questions include the well-posedness of the nonlinear equations, and in which function spaces, the precise regularity of solutions, and the phenomenon of the formation of singularities as compared with the possibility of globally defined evolution in time. One of the main themes will be the close analogy between microlocal techniques for linear PDE and the analysis of nonlinear kinetic equations, through a Wigner and/or a wave packet transform of the solution.


Andrei Biryuk, McMaster & The Fields Institute Frank Merle, Cergy Pontoise, IAS
Jerry Bona, University of Illinois - Chicago Peter Miller, Michigan
Nicolas Burq, Paris-Sud Andrea Nahmod, Massachusetts
Manoussos Grillakis, Maryland Vladislav Panferov, Victoria
Stephen Gustafson, UBC Guido Schneider, Karlsruhe
Slim Ibrahim, McMaster & The Fields Institute Jalal Shatah, CIMS
Niky Kamran, McGill Tai-Peng Tsai, UBC
Markus Keel, Minnesota Luis Vega, Bilbao & IAS
David Lannes, Bordeaux Stephanos Venakides, Duke
Felipe Linares, IMPA Jared Wunsch, Northwestern
Michael Loss, Georgia Tech Doug Wright, McMaster & The Fields Institute
Nader Masmoudi, CIMS Zhengfang Zhou, MSU
Ken McLaughlin, UNC