Date: Tuesday, March 22, 2016
Title: Longtime dynamics and turbulence of nonlinear waves. Part I
Abstract: Nonlinear dispersive waves are partial differential equations that model numerous physical phenomena, ranging from plasma physics, ocean and atmospheric science, to general relativity. Over the past twenty years, the longtime behavior of small amplitude solutions to such equations on Euclidean space (R^n) became relatively wellunderstood. In contrast, the situation is much less understood on bounded domains, that feature a markedly different and rich set of behaviors. In particular, the dynamics in this setting is characterized by outofequilibrium behavior, in the sense that solutions typically do not exhibit longtime stability near equilibrium configurations.
At the level of the physics underlying these problems, studying this outofequilibrium behavior leads to an interesting interplay between dynamics and statistical mechanics, in what is often known as wave turbulence theory. At the level of the mathematics, this study features a beautiful interaction between PDE methods, dynamical systems theory, probability theory, as well as a surprising and very elegant input from analytic number theory.
In this first talk, we shall discuss all these aspects, and survey some recent advances in this direction of research.
Speaker: Zaher Hani
Institution: Georgia Tech
