The regularity of the boundary of vortex patches for some nonlinear transport equations

Abstract

We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in ‫ޒ‬ n with velocity field given by convolution of the density with an odd kernel, homogeneous of degree -(n -1) and of class C 2 ‫ޒ(‬ n \ {0}, ‫ޒ‬ n ).This allows the velocity field to have nontrivial divergence.The quasigeostrophic equation in ‫ޒ‬ 3 and the Cauchy transport equation in the plane are examples.

Locations

• Analysis & PDE - View - PDF
• arXiv (Cornell University) - View - PDF