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

2023/06/06 by Wang, Yuchen, Zhang, Guanghui, Zhou, Maolin · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.03498

Abstract

In this paper, we consider a sign-changing free boundary problem that comes from the boundary regularity of rotating vortex patches of the two-dimensional incompressible Euler equations. The complete classification of singular points has been obtained through establishing a new Weiss-type monotonicity formula. Upon these results, we prove that only 90^∘ corner type of singularity could happen at the boundary of a Lipschitz rotating vortex patch, while the other parts are C^∞ smooth.

Cited by

• Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity
• Finite-time self-similar implosion of hollow vortices

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