1:00 pm Wednesday, November 1, 2017
Analysis Seminar: Global Wellposedness and Scattering for the Davey-Stewartson System at Critical Regularity by Matt Rosenzweig (UT Austin) in RLM 10.176
Over the last twenty years, much work has been devoted to studying long-time dynamics of nonlinear dispersive PDE at regularities which are critical with respect to the scaling invariance of the equations. However, much of this work has focused on equations with algebraic, local nonlinearities. In this talk, I will discuss a particular two-dimensional nonlinear dispersive PDE called the Davey-Stewartson system (DS), which is formally similar to the -critical cubic nonlinear Schrödinger equation (NLS) but differs by an additional nonlocal term. Specifically, I will discuss recent work on the global wellposedness and scattering for a particular case of DS at the critical regularity, which is inspired by Benjamin Dodson's breakthrough work on the cubic NLS. Finally, I will discuss some questions on the rigorous derivation of DS from the free boundary problem describing the evolution of an incompressible, irrotational, and inviscid fluid in a time-dependent domain with fixed bottom. This is a candidacy talk. Submitted by
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