Hölder continuity of solutions for a class of drift-diffusion equations

Abstract

We provide several regularity results for non-homogeneous drift-diffusion equations with applications to general dissipative SQG. Our results unify in a rather simple way several previously known results. We build the estimates on an algebraic identity (for the refined energy argument) which relates any integral operator with pure powers of the laplacian.

Substantial changes. New author (Le Xuan Truong), dealing with general kernels and not only pure powers of the laplacian. The potential estimates will appear in a subsequent work