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

Abstract

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