About: A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying $0 < liminf_{t rightarrow infty} t^gamma \|\|u(t)\|\| le limsup_{t rightarrow infty} t^gamma \|\|u(t)\|\| < infty$ for some $gamma in (0,5/4]$ and prove among others that such solutions, measured in the norm of the Besov space $dot{B}^{-2gamma}_{2,infty}$, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa in cite{Mi} and by Schonbek and Wiegner in cite{SchWi} We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying $0 < liminf_{t rightarrow infty} t^gamma \|\|u(t)\|\| le limsup_{t rightarrow infty} t^gamma \|\|u(t)\|\| < infty$ for some $gamma in (0,5/4]$ and prove among others that such solutions, measured in the norm of the Besov space $dot{B}^{-2gamma}_{2,infty}$, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa in cite{Mi} and by Schonbek and Wiegner in cite{SchWi} (en)
Title	A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces (en)
skos:prefLabel	A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces (en)
skos:notation	RIV/68407700:21110/14:00227614!RIV15-MSM-21110___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	březen
http://linked.open...vai/riv/dodaniDat	2015
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	979
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/14:00227614
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equations; Besov spaces; large-time behavior (en)
http://linked.open.../riv/klicoveSlovo	large-time behavior Navier-Stokes equations Besov spaces
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[F7B690469B3B]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis: Theory, Methods & 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	2014
http://linked.open...v/svazekPeriodika	97
http://linked.open...iv/tvurceVysledku	Skalák, Zdeněk
http://linked.open...ain/vavai/riv/wos	000329114400019
issn	0362-546X
number of pages	6 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.na.2013.11.007
http://localhost/t...ganizacniJednotka	21110

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