Vortex patch solutions to the stationary vortex-wave system
Daomin Cao, Guodong Wang · 2018
The vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is called the background vorticity, and a finite number of concentrated vortices. In this paper we restrict ourselves to the case of a single point vortex in bounded domains. We prove that there exists a steady vortex patch solution to this system with prescribed distribution for the background vorticity. Moreover, we show that these solutions shrink to a minimum point of the Kirchhoff-Routh function as the strength parameter of the background vorticity goes to infinity.