The global regularity of vortex patches revisited

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 C2 off the origin. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

Automated summary

We prove that the regularity of the boundary of vortex patches persists for a large class of transport equations in the plane. The velocity field is constructed by convolving the vorticity with an odd kernel that is homogeneous of degree -1 and belongs to the class C2 away from the origin. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).