$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$

TL;DR

This paper proves that for weak solutions of the Stokes system with drifts in a specific function space, the velocity gradients exhibit reverse H"older inequalities and higher integrability in the $L ext{log}L$ space, advancing regularity theory.

Contribution

It establishes $L ext{log}L$-higher integrability and reverse H"older inequalities for velocity gradients in the Stokes system with drifts in $L_ ext{infty}(BMO^{-1})$, a novel regularity result.

Findings

Proved reverse H"older inequality for velocity gradients.

Established $L ext{log}L$-higher integrability of velocity gradients.

Extended regularity results to drifts in $L_ ext{infty}(BMO^{-1})$.

Abstract

For any weak solution of the Stokes system with drifts in $L_\infty (BMO^{-1})$, we prove a reverse H\"older inequality and $LlogL$-higher integrability of the velocity gradients.