Geodesic
$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 46, Tome 459 (2017), pp. 37-57

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For any weak solution of the Stokes system with drifts in $L_\infty (BMO^{-1})$, we prove a reverse Hölder inequality and $LlogL$-higher integrability of the velocity gradients. 
@article{ZNSL_2017_459_a2,
     author = {J. Burczak and G. Seregin},
     title = {$LlogL$-integrability of the velocity gradient for {Stokes} system with drifts in $L_\infty (BMO^{-1})$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--57},
     publisher = {mathdoc},
     volume = {459},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_459_a2/}
}
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J. Burczak; G. Seregin. $LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 46, Tome 459 (2017), pp. 37-57. http://geodesic.mathdoc.fr/item/ZNSL_2017_459_a2/