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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHaspot, Boris
dc.date.accessioned2020-10-23T10:06:33Z
dc.date.available2020-10-23T10:06:33Z
dc.date.issued2020
dc.identifier.issn0024-6115
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21151
dc.language.isoenen
dc.subjectKorteweg systemen
dc.subject.ddc515en
dc.titleStrong solution for Korteweg system in bmo−1(\RN) with initial density in L∞en
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we investigate the question of the existence of strong solution in finite time for the Korteweg system for small initial data provided that the initial momentum ρ 0 u 0 belongs to bmo −1 T (R N) for T > 0 and the initial density ρ 0 is in L ∞ (R N) with N ≥ 1 and far away from the vacuum. This result extends the so called Koch-Tataru theorem for the Korteweg system. It is also interesting to observe that any initial shock on the density is instantaneously regularized inasmuch as the density becomes Lipschitz for any ρ(t, ·) with t > 0. We also prove the existence of global strong solution for initial data (ρ 0 − 1, ρ 0 u 0) ∈ (B N 2 −1 2,∞ (R N) ∩ B N 2 2,∞ (R N)∩L ∞ (R N))×(B N 2 −1 2,∞ (R N)) N. This result allows in particular to extend the notion of Oseen solution (corresponding to particular solution of the incompressible Navier Stokes system in dimension N = 2) to the Korteweg system provided that the vorticity of the momentum ρ 0 u 0 is a Dirac mass αδ 0 with α sufficiently small. IHowever unlike the Navier Stokes equations the property of self similarity is not conserved for the Korteweg system since there is no invariance by scaling because the term of pressure.en
dc.relation.isversionofjnlnameProceedings of the London Mathematical Society
dc.relation.isversionofjnlvol121en
dc.relation.isversionofjnlissue6en
dc.relation.isversionofjnldate2020-09
dc.relation.isversionofjnlpages1766-1797en
dc.relation.isversionofdoi10.1112/plms.12370en
dc.relation.isversionofjnlpublisherWileyen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2020-10-23T10:02:43Z
hal.author.functionaut


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