Existence and uniqueness of planar vortex patch in incompressible steady flow

In this talk, we consider the planar vortex patch problem in an incompressible steady flow in a bounded domain $\mathbb R^2$. We will talk about the existence, the asymptotic behaviour and the uniqueness of the steady flow. This talk is based on the joint works with Daomin Cao, Yuxia Guo and Shusen Yan.