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

Yuchen Wang; Guanghui Zhang; Maolin Zhou

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

Analysis of PDEs 2026-04-30 v5

Authors: Yuchen Wang , Guanghui Zhang , Maolin Zhou

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 $90^\circ$ corner near singular boundary points, if the patch is Lipschitz.

Keywords

vortex patches free boundary problem euler equations boundary regularity corner singularity

Cite

@article{arxiv.2306.03498,
  title  = {Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem},
  author = {Yuchen Wang and Guanghui Zhang and Maolin Zhou},
  journal= {arXiv preprint arXiv:2306.03498},
  year   = {2026}
}

Comments

28 pages, accepted by AIHPC

Related papers

View all related →