|Date: Thursday, March 24, 2016
Location: 4088 East Hall (4:00 PM to 5:00 PM)
Title: Long-time dynamics and turbulence of nonlinear waves: Part III. Dynamical Approach
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 long-time behavior of small amplitude solutions to such equations on Euclidean space (R^n) became relatively well-understood. 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 out-of-equilibrium behavior, in the sense that solutions typically do not exhibit long-time stability near equilibrium configurations.
At the level of the physics underlying these problems, studying this out-of-equilibrium 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 talk, we will adopt a dynamical systems approach, and construct solutions that exhibit this out-of-equilibrium behavior in a quantitative manner.
Speaker: Zaher Hani
Institution: Georgia Tech