Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
数学专题报告
报告题目(Title)：Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
报告人(Speaker)：童嘉骏 (BICMR, 北京大学)
地点(Place)： 后主楼 1220
时间(Time)： 2024 年 12 月 11 日（周三） 9:00--10:00
邀请人(Inviter)：薛留堂
报告摘要
It is of great mathematical and physical interest to study traveling wave solutions to the 2D incompressible Euler equation in the form of a touching pair of symmetric vortex patches with opposite signs. Such a solution was numerically illustrated by Sadovskii in 1971, but its rigorous existence was left as an open problem. In this talk, we will rigorously construct such a solution by a novel fixed-point approach that determines the patch boundary as a fixed point of a nonlinear map. Smoothness and other properties of the patch boundary will also be characterized. This is based on a joint work with De Huang.
