arXiv:2211.07808 Abstract | arXiv Analytics

arXiv:2211.07808 [math.AP]Abstract References Reviews Resources

Existence and Regularity for Vortex Patch Solutions of the 2D Euler Equations

Published 2022-11-15Version 1

In "Global regularity for vortex patches" (Commun. Math. Phys. 1993), Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H\"older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.

Categories: math.AP

Subjects: 35Q31, 35Q35, 76B47

Keywords: 2d euler equations, vortex patch solutions, level-set framework, vortex patch problem, global regularity

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