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Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system

dc.contributor.authorHaspot, Boris
dc.contributor.authorCharve, Frédéric
dc.date.accessioned2011-10-27T10:16:58Z
dc.date.available2011-10-27T10:16:58Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7343
dc.language.isoenen
dc.subjectKorteweg systemen
dc.subjectstrong solutionen
dc.subjectvanishing capillarity-viscosityen
dc.subjectcompressible Euler systemen
dc.subject.ddc515en
dc.titleExistence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg systemen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire d'Analyse et de Mathématiques Appliquées (LAMA) http://umr-math.univ-mlv.fr/ CNRS : UMR8050 – Université Paris-Est – Université Paris XII Val de Marne;France
dc.description.abstractenIn the first part of this paper, we prove the existence of global strong solution for Korteweg system in one dimension. In the second part, motivated by the processes of vanishing capillarity-viscosity limit in order to select the physically relevant solutions for a hyperbolic system, we show that the global strong solution of the Korteweg system converges in the case of a $\gamma$ law for the pressure ($P(\rho)=a\rho^{\gamma}$, $\gamma>1$) to entropic solution of the compressible Euler equations. In particular it justifies that the Korteweg system is suitable for selecting the physical solutions in the case where the Euler system is strictly hyperbolic. The problem remains open for a Van der Waals pressure because in this case the system is not strictly hyperbolic and in particular the classical theory of Lax and Glimm (see \cite{Lax,G}) can not be used.en
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol45
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages469-494
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/120861801
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00635983/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAM
dc.subject.ddclabelAnalyseen


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