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dc.contributor.authorHaspot, Boris
dc.date.accessioned2018-09-06T09:18:21Z
dc.date.available2018-09-06T09:18:21Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17968
dc.language.isoenen
dc.subjectNavier-Stokes equationsen
dc.subject.ddc515en
dc.titleVortex solutions for the compressible Navier-Stokes equations with general viscosity coefficients in 1D: regularizing effects or not on the densityen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider Navier-Stokes equations for compressible viscous fluids in the one-dimensional case with general viscosity coefficients. We prove the existence of global weak solution when the initial momentum ρ 0 u 0 belongs to the set of the finite measure M(R) and when the initial density ρ 0 is in the set of bounded variation functions BV (R). In particular it includes at the same time the case of initial momentum which are Dirac masses and initial density which admit shocks. We can observe in particular that this type of initial data have infinite energy. Furthermore we show that if the coupling between the density and the velocity is sufficiently strong then the initial density which admits initially shocks is instantaneously regularizing and becomes continuous. This coupling is expressed via the regularity of the so called effective velocity v = u + µ(ρ) ρ 2 ∂ x ρ (see [20, 18, 3]) with µ(ρ) the viscosity coefficient. Inversely if the coupling between the initial density and the initial velocity is to weak (it means ρ 0 v 0 ∈ M(R)) then we prove the existence of weak energy in finite time but the density remains a prirori discontinuous on the time interval of existence.en
dc.identifier.citationpages44en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01716150en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2018-03
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-09-06T09:14:05Z
hal.person.labIds60


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