Steady vortex patches near a nontrivial irrotational flow
arXiv:1902.07396 · doi:10.1007/s11425-018-9495-1
Abstract
In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extremum points of on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of corresponds to a family of steady multiple vortex patches approaching it.
21 pages