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Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem

  • Yuchen Wang

    Tianjin Normal University, P. R. China

  • Guanghui Zhang

    Huazhong University of Science and Technology, Wuhan, P. R. China

  • Maolin Zhou

    Nankai University, Tianjin, P. R. China
Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem cover
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Abstract

In this paper, we consider the sign-changing free boundary problem related to the uniformly rotating vortex patch solutions of the two-dimensional incompressible Euler equations. We prove that the boundary of the vortex patch locally forms a corner near singular boundary points, if the patch is Lipschitz.

Cite this article

Yuchen Wang, Guanghui Zhang, Maolin Zhou, Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2026), published online first

DOI 10.4171/AIHPC/183