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

Razvan-Octavian Radu

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arXiv · 2211.07808

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

Razvan-Octavian Radu

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Abstract

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.

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Razvan-Octavian Radu. 2022-11-15. Existence and Regularity for Vortex Patch Solutions of the 2D Euler Equations. https://arxiv.org/abs/2211.07808

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