Potential Theory for Nonlocal Drift-Diffusion Equations

Abstract

The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to include drifts of critical order belonging merely to BMO. In particular, our results allow us to derive new estimates for the dissipative surface quasi-geostrophic equation.