Existence and uniqueness of vortex patch for two dimensional Euler equation

In this talk, the speaker will talk about the results obtained in recent years on the existence and uniqueness of  vortex patch for two dimensional imcompressible Euler equation. It turns out that the number of vortex patch concentrated near some points is closely related to the number of critical points of the so-called Kirchhoff-Routh function, which is determined by the Green's function of the domain on which the equation is set on. The talk is based on results of papers with Yuxia Guo, Shuangjie Peng and Shusen Yan.