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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 459, Pages 37–57 (Mi znsl6463)  
$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$

J. Burczakab, G. Seregincd

a Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
b Mathematical Institute, University of Oxford, UK
c Oxford University, UK
d St. Petersburg Department of Steklov Mathematical Institute, RAS, Russia
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Abstract: 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.
Key words and phrases: Stokes system with drift, reverse Hölder inequality, higher integrability.
Funding agency Grant number
MNiSW 1289/MOB/IV/2015/0
Russian Foundation for Basic Research 17-01-00099-a
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
J. Burczak was supported by MNiSW "Mobilność Plus" grant 1289/MOB/IV/2015/0. G. Seregin was supported in parts by the grant RFBR 17-01-00099-a and by the Program of the Presidium of the Russian Academy of Sciences No. 1 “Fundamental Mathematics and its Applications” under grant PRAS-18-01.
Received: 18.07.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 236, Issue 4, Pages 399–412
DOI: https://doi.org/10.1007/s10958-018-4120-6
Document Type: Article
UDC: 517
Language: English
Citation: J. Burczak, G. Seregin, “$LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$”, Boundary-value problems of mathematical physics and related problems of function theory. Part 46, Zap. Nauchn. Sem. POMI, 459, POMI, St. Petersburg, 2017, 37–57; J. Math. Sci. (N. Y.), 236:4 (2019), 399–412
Citation in format AMSBIB
\Bibitem{BurSer17}
\by J.~Burczak, G.~Seregin
\paper $LlogL$-integrability of the velocity gradient for Stokes system with drifts in $L_\infty (BMO^{-1})$
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~46
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 459
\pages 37--57
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6463}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 236
\issue 4
\pages 399--412
\crossref{https://doi.org/10.1007/s10958-018-4120-6}
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