Vortex patch motion in bounded domains
数学专题报告
报告题目(Title)：Vortex patch motion in bounded domains
报告人(Speaker)：Emeric Roulley (SISSA, Trieste, Italy)
地点(Place)：Zoom 会议 ID：862 848 65881 , 密码：123456, Zoom Link: https://us02web.zoom.us/j/86284865881
时间(Time)：2024 年 9 月 27 日（周五） 16:00--17:00
邀请人(Inviter)：薛留堂
报告摘要
We consider the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the single point vortex, under certain non-degeneracy conditions, it is possible to desingularize most of these trajectories into time-periodic concentrated vortex patches. We provide concrete examples of these non-degeneracy conditions, which are satisfied by a broad class of domains, including convex ones. The proof uses Nash-Moser scheme and KAM techniques combined with complex geometry tools. Additionally, we will present a vortex duplication mechanism to generate synchronized time-periodic motion of multiple vortices.
