Existence and regularity for vortex patch solutions of the 2D Euler equations

Abstract

. In [3], 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.