Date: Thursday, March 24, 2016
Location: 4088 East Hall (4:00 PM to 5:00 PM)
Title: Longtime 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 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 talk, we will adopt a dynamical systems approach, and construct solutions that exhibit this outofequilibrium behavior in a quantitative manner.
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Speaker: Zaher Hani
Institution: Georgia Tech
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