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A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
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SYSNO ASEP 0440826 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve SCOPUS Title A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations Author(s) Neustupa, Jiří (MU-W) RID, SAI, ORCID Source Title Mathematica Bohemica. - : Matematický ústav AV ČR, v. v. i. - ISSN 0862-7959
Roč. 139, č. 4 (2014), s. 685-698Number of pages 14 s. Language eng - English Country CZ - Czech Republic Keywords Navier-Stokes equation ; suitable weak solution ; regularity Subject RIV BA - General Mathematics R&D Projects GA13-00522S GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 EID SCOPUS 84929353254 Annotation We deal with a suitable weak solution $(bold v,p)$ to the Navier-Stokes equations in a domain $Omegasubsetmathbb R^3$. We refine the criterion for the local regularity of this solution at the point $(bold fx_0,t_0)$, which uses the $L^3$-norm of $bold v$ and the $L^{3/2}$-norm of $p$ in a shrinking backward parabolic neighbourhood of $(bold x_0,t_0)$. The refinement consists in the fact that only the values of $bold v$, respectively $p$, in the exterior of a space-time paraboloid with vertex at $(bold x_0,t_0)$, respectively in a "small" subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point $(bold x_0,t_0)$ if $bold v$ and $p$ are "smooth" outside the paraboloid. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2015
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