About: Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator

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About: Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We show that there exist solutions of the Navier-Stokes initial-boundary value problem such that their initial value is arbitrarily large (in the graph norm of fractional power between 1/4 and 1/2 of the Stokes operator) and they belong to an arbitrary chosen open set in the domain of the fractional power between 3/4 and 1 of the Stokes operator at a time instant which can be as small as we wish. As an auxiliary result, we prove the theorem on stability of a strong solution with respect to certain norm induced by a fractional power of the Stokes operator. We show that there exist solutions of the Navier-Stokes initial-boundary value problem such that their initial value is arbitrarily large (in the graph norm of fractional power between 1/4 and 1/2 of the Stokes operator) and they belong to an arbitrary chosen open set in the domain of the fractional power between 3/4 and 1 of the Stokes operator at a time instant which can be as small as we wish. As an auxiliary result, we prove the theorem on stability of a strong solution with respect to certain norm induced by a fractional power of the Stokes operator. (en) Ukazujeme, že existují řešení Navierova-Stokesova počátečního-okrajového problému taková, že jejich počáteční hodnota je libovolně velká (v grafové normě necelé mocniny mezi 1/4 a 1/2 Stokesova operátoru) a patří do libovolné otevřené množiny v definičním oboru mocniny mezi 3/4 a 1 Stokesova operátoru v časovém okamžiku, který může být libovolně malý. Jako pomocný výsledek dokazujeme větu o stabilitě silného řešení v normě indukované necelou mocninou Stokesova operátoru. (cs)
Title	Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator (en) Silné řešení Navierových-Stokesových rovnic s velkou počáteční rychlostí v definičním oboru necelých mocnin Stokesova operátoru (cs)
skos:prefLabel	Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator (en) Silné řešení Navierových-Stokesových rovnic s velkou počáteční rychlostí v definičním oboru necelých mocnin Stokesova operátoru (cs)
skos:notation	RIV/68407700:21220/06:02121170!RIV07-MSM-21220___
http://linked.open.../vavai/riv/strany	260;265
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190612), Z(MSM6840770010)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2007
http://linked.open...aciTvurceVysledku	Neustupa, Jiří Kučera, Petr
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	České vysoké učení technické v Praze / Fakulta strojní
http://linked.open...dnocenehoVysledku	501874
http://linked.open...ai/riv/idVysledku	RIV/68407700:21220/06:02121170
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equation; Stokes operator; strong solution (en)
http://linked.open.../riv/klicoveSlovo	Stokes operator strong solution Navier-Stokes equation
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[A821DEC7CE66]
http://linked.open...i/riv/nazevZdroje	WSEAS Transactions on Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Regularity and other qualitative properties of solutions to the Navier-Stokes and related equations, transition to turbulence.
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	5
http://linked.open...iv/tvurceVysledku	Kučera, Petr Neustupa, Jiří
http://linked.open...n/vavai/riv/zamer	Aplikovaná matematika v technických a fyzikálních vědách
issn	1109-2769
number of pages	6 (xsd:int)
http://localhost/t...ganizacniJednotka	21220
is http://linked.open...avai/riv/vysledek of	Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator Strong Solution of the Navier-Stokes Equation with Large Initial Velocity in Domain of a Fractional Power of the Stokes Operator

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