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

Yuchen Wang; Guanghui Zhang; Maolin Zhou

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arXiv · 2306.03498

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

Yuchen Wang·Guanghui Zhang·Maolin Zhou

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

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Yuchen Wang, Guanghui Zhang, Maolin Zhou. 2023-06-06. Boundary regularity of uniformly rotating vortex patches and an unstable elliptic free boundary problem. https://arxiv.org/abs/2306.03498

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