Analysis Seminar

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Recent progress in nonlinear inviscid damping for two dimensional incompressible Euler equation

Speaker: Hao Jia, University of Minnesota

Location: Warren Weaver Hall 1314

Date: Thursday, November 21, 2019, 9:45 a.m.

Synopsis:

Inviscid damping is a fundamental relaxation mechanism for
two dimensional Euler equation. Recently there have been significant
advances in understanding linear inviscid damping in Sobolev spaces
for shear flows and vortices. Extending the linear analysis to
nonlinear analysis is challenging since the rate of stabilization is
slow, convergence of vorticity field only holds in weak
distributional sense and the effect of nonlinearity is strong. So
far there are only very few results proving full nonlinear inviscid
damping, which include Bedrossian and Masmoudi's breakthrough work
on Couette flow, and Ionescu and J.'s recent work on
axi-symmetrization of vorticity near point vortex solutions. In this
talk, we will discuss some recent progress, that aims to study more
general flows. Based on joint work with Alex Ionescu.