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dc.contributor.authorMelinand, Benjamin
dc.contributor.authorZumbrun, Kevin
dc.date.accessioned2019-11-20T11:45:24Z
dc.date.available2019-11-20T11:45:24Z
dc.date.issued2019
dc.identifier.issn01672789
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20223
dc.language.isoenen
dc.subjectStability of steady wavesen
dc.subjectBounded domainsen
dc.subjectIsentropic gasen
dc.subjectEvans functionen
dc.subject.ddc515en
dc.titleExistence and stability of steady compressible Navier–Stokes solutions on a finite interval with noncharacteristic boundary conditionsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study existence and stability of steady solutions of the isentropic compressible Navier–Stokes equations on a finite interval with noncharacteristic boundary conditions, for general not necessarily small-amplitude data. We show that there exists a unique solution, about which the linearized spatial operator possesses (i) a spectral gap between neutral and growing/decaying modes, and (ii) an even number of nonstable eigenvalues (with a nonnegative real part). In the case that there are no nonstable eigenvalues, i.e., of spectral stability, we show this solution to be nonlinearly exponentially stable in . Using “Goodman-type” weighted energy estimates, we establish spectral stability for small-amplitude data. For large-amplitude data, we obtain high-frequency stability, reducing stability investigations to a bounded frequency regime. On this remaining, bounded-frequency regime, we carry out a numerical Evans function study, with results again indicating universal stability of solutions.en
dc.relation.isversionofjnlnamePhysica D: Nonlinear Phenomena
dc.relation.isversionofjnlvol394en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2019-07
dc.relation.isversionofjnlpages16-25en
dc.relation.isversionofdoi10.1016/j.physd.2019.01.006en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01625910v1en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2019-11-20T11:42:17Z
hal.person.labIds60
hal.person.labIds121644


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