Existence and regularity for perturbed Stokes system with critical drift in 2D

Paper

Abstract

We consider a perturbed Stokes system with critical divergence-free drift in a bounded Lipschitz domain in

, with sufficiently small Lipschitz constant L. It extends our previous work in

, to two-dimensional case. For large drift in weak

space, we prove unique existence of q-weak solutions for force in

with q close to 2. Moreover, for drift in

we prove the unique existence of

solutions for arbitrarily large L. Using similar methods we can also prove analogous results for scalar equations with divergence-free drifts in weak

space.