About: A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

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About: A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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 %22small%22 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 %22smooth%22 outside the paraboloid. 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 %22small%22 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 %22smooth%22 outside the paraboloid. (en)
Title	A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations (en)
skos:prefLabel	A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations (en)
skos:notation	RIV/67985840:_____/14:00440826!RIV15-GA0-67985840
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA13-00522S)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Neustupa, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	752
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/14:00440826
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equation; suitable weak solution; regularity (en)
http://linked.open.../riv/klicoveSlovo	suitable weak solution regularity Navier-Stokes equation
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[BF63873FEE7F]
http://linked.open...i/riv/nazevZdroje	Mathematica Bohemica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Qualitative analysis and numerical solution of problems of flows in generally time-dependent domains with various boundary conditions
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	139
http://linked.open...iv/tvurceVysledku	Neustupa, Jiří
issn	0862-7959
number of pages	14 (xsd:int)

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