## Formation of small scales in nonlinear PDEs

### Linear inviscid damping in Gevrey spaces

Hao Jia

University of Minnesota

Abstract:

Inviscid damping is a fundamental relaxation mechanism for two dimensional Euler equation. There has been significant progress on linear inviscid damping for shear flows and vortices in Sobolev spaces of limited regularity. However the only known techniques in establishing nonlinear inviscid damping depend on Gevrey spaces which involve very smooth functions. In this talk, we discuss a recent result proving linear inviscid damping in Gevrey spaces, which can be viewed as a step towards nonlinear inviscid damping for general shear flows.