About: Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua

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About: Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The Navier Stokes equations for a compressible barotropic fluid in 1D with zero velocity boundary conditions are considered. We study the case of large initial data in Hi as well as the mass force such that the stationary density is uniquely determined but admits vacua. Missing uniform lower bound for the density is compensated by a careful modification of the construction procedure for a Lyapunov functional known for the case of solutions which are globally away from zero [I. Straskraba, A.A. Zlotnik. On a decay rate for 1D-viscous compressible barotropic fluid equations, J. Evol. Equ. 2 (2002) 69-96]. An immediate consequence of this construction is a decay rate estimate for this highly singular problem. The results are proved in the Eulerian coordinates for a large class of increasing state functions including rho(rho) = a rho(gamma) with any gamma > 0 (a > 0 a constant). The Navier Stokes equations for a compressible barotropic fluid in 1D with zero velocity boundary conditions are considered. We study the case of large initial data in Hi as well as the mass force such that the stationary density is uniquely determined but admits vacua. Missing uniform lower bound for the density is compensated by a careful modification of the construction procedure for a Lyapunov functional known for the case of solutions which are globally away from zero [I. Straskraba, A.A. Zlotnik. On a decay rate for 1D-viscous compressible barotropic fluid equations, J. Evol. Equ. 2 (2002) 69-96]. An immediate consequence of this construction is a decay rate estimate for this highly singular problem. The results are proved in the Eulerian coordinates for a large class of increasing state functions including rho(rho) = a rho(gamma) with any gamma > 0 (a > 0 a constant). (en)
Title	Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua (en)
skos:prefLabel	Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua (en)
skos:notation	RIV/67985840:_____/10:00352455!RIV11-GA0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/08/0012), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Straškraba, Ivan
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	251903
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00352455
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	compressible fluid; Navier-Stokes equations; asymptotic behavior (en)
http://linked.open.../riv/klicoveSlovo	asymptotic behavior compressible fluid Navier-Stokes equations
http://linked.open...odStatuVydavatele	FR - Francouzská republika
http://linked.open...ontrolniKodProRIV	[B4B424EDF615]
http://linked.open...i/riv/nazevZdroje	Bulletin Des Sciences Mathematiques
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Qualitative analysis and numerical solution of flow problems
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	134
http://linked.open...iv/tvurceVysledku	Penel, P. Straškraba, Ivan
http://linked.open...ain/vavai/riv/wos	000276938900004
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0007-4497
number of pages	17 (xsd:int)

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