This volume is a special issue of the Quarterly of Applied Mathematics journal. It represents the proceedings of the conference in honor of Walter Strauss's 70th birthday held at Brown University (Providence, RI) in May of 2008. The issue offers a collection of original and expository articles devoted to the study of nonlinear wave equations. The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid mechanics, kinetic theory, and stability theory. The book offers a nice cross-section of current trends and research directions in the study of nonlinear wave equations.

Published by Brown University and distributed worldwide by the American Mathematical Society.

Table of Contents

• Y. Guo -- Introduction to the Brown University Nonlinear Wave Equations Conference papers
• C. Morawetz -- Introduction. Dinner speech
• M. Grillakis -- The mathematics of W. A. Strauss and his contributions to analysis
• H. Andréasson, M. Kunze, and G. Rein -- Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system
• C. Bardos and N. J. Mauser -- One particle equations for many particle quantum systems: The MCTHDF method
• N. Burq, P. Gérard, and N. Tzvetkov -- High frequency solutions of the nonlinear Schrödinger equation on surfaces
• G.-Q. Chen, M. Slemrod, and D. Wang -- A fluid dynamic formulation of the isometric embedding problem in differential geometry
• A. Constantin -- On the particle paths in solitary waves
• W. Craig and C. Sulem -- Asymptotics of surface waves over random bathymetry
• J. Ginibre and G. Velo -- Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations
• R. Glassey, J. Schaeffer, and S. Pankavich -- Time decay for solutions to one-dimensional two component plasma equations
• Y. Guo -- Bounded solutions for the Boltzmann equation
• Y. Guo and Y. Han -- Critical Rayleigh number in Rayleigh-Bénard convection
• J. Shatah -- Space-time resonances
• T. C. Sideris -- Energy splitting for solutions of multi-dimensional isotropic symmetric hyperbolic equations