About: The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In the paper we study the large-time behavior of solutions to the Navier-Stokes equations in the frequency space. We describe in detail the large-time energy concentration which occurs in every (turbulent) solution. If the energy of the solution decreases exponentially then it concentrates in frequencies localized in an annulus in the frequency space. The annulus can be taken arbitrarily narrow and its diameter determines the rate of the exponential decay. All the other solutions are characterized by the concentration of the energy in the frequencies localized in a ball with an arbitrarily small diameter centered in the origin of the coordinates. It will follow from the presented results that the frequencies outside the annulus or the ball and especially the higher frequencies die out very quickly. We will further observe the concentration occurring in any time derivative of the solution or in the vorticity and its time derivatives with the same annulus or the ball for the particular solution In the paper we study the large-time behavior of solutions to the Navier-Stokes equations in the frequency space. We describe in detail the large-time energy concentration which occurs in every (turbulent) solution. If the energy of the solution decreases exponentially then it concentrates in frequencies localized in an annulus in the frequency space. The annulus can be taken arbitrarily narrow and its diameter determines the rate of the exponential decay. All the other solutions are characterized by the concentration of the energy in the frequencies localized in a ball with an arbitrarily small diameter centered in the origin of the coordinates. It will follow from the presented results that the frequencies outside the annulus or the ball and especially the higher frequencies die out very quickly. We will further observe the concentration occurring in any time derivative of the solution or in the vorticity and its time derivatives with the same annulus or the ball for the particular solution (en)
Title	The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space (en)
skos:prefLabel	The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space (en)
skos:notation	RIV/68407700:21110/13:00204172!RIV14-MSM-21110___
http://linked.open...avai/predkladatel	Fakulta stavební
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	2
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	České vysoké učení technické v Praze / Fakulta stavební
http://linked.open...dnocenehoVysledku	84323
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/13:00204172
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equations; large-time behavior of solutions; energy concentration (en)
http://linked.open.../riv/klicoveSlovo	energy concentration Navier-Stokes equations large-time behavior of solutions
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[C072DB19B9D1]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Analysis and Its Applications
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...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	400
http://linked.open...iv/tvurceVysledku	Skalák, Zdeněk
http://linked.open...ain/vavai/riv/wos	000314075600034
issn	0022-247X
number of pages	21 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jmaa.2012.11.004
http://localhost/t...ganizacniJednotka	21110

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