About: The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces

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About: The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	It is known that the turbulent solutions to the unforced Navier-Stokes equations exhibit a large-time energy concentration in the frequency space. If we suppose the existence of a nonzero time dependent external force f is an element of L-1((0, infinity); L-sigma(2)) in the equations, the situation is more complicated. It is possible to construct simple examples of solutions, in which the energy is asymptotically distributed over the entire spectrum of the Stokes operator. Further, we will show as the main result of this paper that there still exist wide classes of initial conditions and external forces yielding solutions with the large-time energy concentration analogical to the situation in the unforced Navier-Stokes equations. We will also show that the frequency spectrum of the solution does not generally relate to the frequency spectrum of the external force. It is known that the turbulent solutions to the unforced Navier-Stokes equations exhibit a large-time energy concentration in the frequency space. If we suppose the existence of a nonzero time dependent external force f is an element of L-1((0, infinity); L-sigma(2)) in the equations, the situation is more complicated. It is possible to construct simple examples of solutions, in which the energy is asymptotically distributed over the entire spectrum of the Stokes operator. Further, we will show as the main result of this paper that there still exist wide classes of initial conditions and external forces yielding solutions with the large-time energy concentration analogical to the situation in the unforced Navier-Stokes equations. We will also show that the frequency spectrum of the solution does not generally relate to the frequency spectrum of the external force. (en)
Title	The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces (en)
skos:prefLabel	The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces (en)
skos:notation	RIV/67985874:_____/13:00395206!RIV14-AV0-67985874
http://linked.open...avai/predkladatel	Ústav pro hydrodynamiku AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Skalák, Zdeněk
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	Ústav pro hydrodynamiku AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	84324
http://linked.open...ai/riv/idVysledku	RIV/67985874:_____/13:00395206
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	the Navier-Stokes equations; external forces; energy concentration in frequency space (en)
http://linked.open.../riv/klicoveSlovo	energy concentration in frequency space external forces the Navier-Stokes equations
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[291E86F66622]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Analysis and Applications
http://linked.open...in/vavai/riv/obor	BK
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	402
http://linked.open...iv/tvurceVysledku	Skalák, Zdeněk
http://linked.open...ain/vavai/riv/wos	000315836900013
issn	0022-247X
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jmaa.2013.01.010

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