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Steady vortex patches near a nontrivial irrotational flow

Analysis of PDEs 2019-05-23 v1

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 qq corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extremum points of qq on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of qq corresponds to a family of steady multiple vortex patches approaching it.

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Cite

@article{arxiv.1902.07396,
  title  = {Steady vortex patches near a nontrivial irrotational flow},
  author = {Daomin Cao and Guodong Wang and Weicheng Zhan},
  journal= {arXiv preprint arXiv:1902.07396},
  year   = {2019}
}

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21 pages