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Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 119–128 (Mi znsl6740)  

Regularity of solutions to the Navier–Stokes equations in $\dot{B}_{\infty,\infty}^{-1}$

G. Seregina, D. Zhoub

a Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
b School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, P. R. China

Abstract: We prove that if $u$ is a suitable weak solution to the three dimensional Navier–Stokes equations from the space $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, then all scaled energy quantities of $u$ are bounded. As a consequence, it is shown that any axially symmetric suitable weak solution $u$, belonging to $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, is smooth.

Key words and phrases: Navier–Stokes equations, suitable weak solutions, Besov spaces.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
The first author is supported by the Program of the Presidium of the Russian Academy of Sciences No. 01 ``Fundamental Mathematics and its Applications'' under grant PRAS-18-01.


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Received: 29.11.2018
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Citation: G. Seregin, D. Zhou, “Regularity of solutions to the Navier–Stokes equations in $\dot{B}_{\infty,\infty}^{-1}$”, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Zap. Nauchn. Sem. POMI, 477, POMI, St. Petersburg, 2018, 119–128

Citation in format AMSBIB
\Bibitem{SerZho18}
\by G.~Seregin, D.~Zhou
\paper Regularity of solutions to the Navier--Stokes equations in $\dot{B}_{\infty,\infty}^{-1}$
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 477
\pages 119--128
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6740}


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