Global Existence and Uniqueness of Unbounded Solutions in the 2D Euler Equations
数学专题报告
报告题目(Title)：Global Existence and Uniqueness of Unbounded Solutions in the 2D Euler Equations
报告人(Speaker)：Dimitri Cobb (University of Bonn)
地点(Place)：Zoom 会议 ID：862 042 00061 , 密码：123456, Zoom Link: https://us02web.zoom.us/j/86204200061
时间(Time)：2025 年 03 月 25 日（周二） 16:00--17:00
邀请人(Inviter)：薛留堂
报告摘要
In this talk, we will study unbounded solutions of the incompressible
Euler equations in two dimensions of space. The main interest of these
solutions is that the usual function spaces in which solutions are defined
(for example based on finite energy conditions like $L^2$ or $H^s$) are
not compatible with the symmetries of the problem, namely Galileo
invariance and scaling transformation. In addition, many real world
problems naturally involve infinite energy solutions, typically in
geophysics.
After presenting the problem and giving an overview of previous results,
we will state our result: existence and uniqueness of global Yudovich
solutions under a certain sublinear growth assumption of the initial data.
The proof is based on an integral decomposition of the pressure and local
energy balance, leading to global estimates in local Morrey spaces.
This work was done in collaboration with Herbert Koch (Universität Bonn).
