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Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua
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SYSNO ASEP 0352455 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Construction of a Lyapunov functional for 1D-viscous compressible barotropic fluid equations admitting vacua Author(s) Penel, P. (FR)
Straškraba, Ivan (MU-W) RID, SAISource Title Bulletin des Sciences Mathématiques. - : Elsevier - ISSN 0007-4497
Roč. 134, č. 3 (2010), s. 278-294Number of pages 17 s. Language eng - English Country FR - France Keywords compressible fluid ; Navier-Stokes equations ; asymptotic behavior Subject RIV BA - General Mathematics R&D Projects GA201/08/0012 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000276938900004 EID SCOPUS 77949569419 DOI 10.1016/j.bulsci.2009.02.003 Annotation 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). Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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