Existence and regularity for perturbed Stokes system with critical drift

Abstract

We consider the existence and $L^q$ gradient estimates for perturbed Stokes systems with divergence-free critical drift in a bounded Lipschitz domain in ${\mathbb{R}}^n$, $n\ge 3$. The first two results assume the drift is either in $L^n$ or sufficiently small in weak $L^n$. The third result assumes the drift is in weak $L^n$ without smallness, and obtain results for $q$ close to 2.

Comm. Partial Differential Equations, accepted