Periodic solutions around localized radial profiles for the 2D Euler equations
数学专题报告
报告题目(Title)：Periodic solutions around localized radial profiles for the 2D Euler equations
报告人(Speaker)：Claudia Garcia (西班牙Granada大学)
地点(Place)：Zoom 会议 ID：965 896 06660, 密码：123456, Zoom Link: https://zoom.us/j/96589606660
时间(Time)：2023 年 12 月 20 日（周三） 16:00--17:00
邀请人(Inviter)：薛留堂
报告摘要
In this talk, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type $f_0(|x|)$ supported on the unit disk, with $f_0$ being a strictly monotonic profile with constant sign. We distinguish two scenarios according to the sign of the profile: defocusing and focusing. In the first regime, we have scarcity of the bifurcating curves associated with lower symmetry. However, in the focusing case we get a countable family of bifurcating solutions associated with large symmetry. The approach developed in this work is new and flexible, and the explicit expression of the radial profile $f_0$ is no longer required as in previous works. The alternative for that is a refined study of the associated spectral problem based on Sturm-Liouville differential equation with a variable potential that changes the sign depending on the shape of the profile and the location of the time period.
