The global regularity of vortex patches revisited

Abstract

We prove persistence of the regularity of the boundary of vortex patches for a large class of transport equations in the plane. The velocity field is given by convolution of the vorticity with an odd kernel, homogeneous of degree $-1$ and of class $C^2$ off the origin.

arXiv commentSome inaccuracies corrected, in particular one in the statement of Lemma 3

References in corpus (1)

• The regularity of the boundary of vortex patches for some non-linear transport equations

Cited by in corpus (1)

• The $\alpha$-SQG patch problem is illposed in $C^{2,\beta }$ and $W^{2,p}$