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Existence of steady symmetric vortex patch in a disk

Analysis of PDEs 2019-09-04 v2

Abstract

In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational problem in which the kinetic energy of the fluid is maximized subject to some appropriate constraints for the vorticity. Moreover, we show that these vortex patches shrink to a given minimum point of the corresponding Kirchhoff-Routh function as the vorticity strength parameter goes to infinity.

Keywords

Cite

@article{arxiv.1807.02993,
  title  = {Existence of steady symmetric vortex patch in a disk},
  author = {Daomin Cao and Guodong Wang and Bijun Zuo},
  journal= {arXiv preprint arXiv:1807.02993},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-23T02:54:30.493Z