Speaker：Yuchen Wang (Central China Normal University)

Time：2022-12-08, 15:00

Location：Tencent Meeting ID：852 727 978（No Password）

Abstract:

In this talk, we shall focus on a special class of vortex structures in inviscid fluids called concentrated vorticity, in which the vortical domain is compactly supported in some small regions.  Through a perturbative argument, we prove the existence of steady solutions of the 2-D incompressible Euler equation which are highly concentrated near some given points, and obtain a more precise leading tern.  These solutions are locally unique with prescribed vortex profiles. Moreover, we study the local dynamics on vortex patches and obtain exponential trichotomy on the linearized patch dynamics. We shall also report some results on the 2-D capillary-gravity waves and gSQG equation.