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hal.structure.identifierLaboratoire Jacques-Louis Lions [LJLL]
dc.contributor.authorAudiard, Corentin
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHaspot, Boris
dc.date.accessioned2018-01-15T15:43:23Z
dc.date.available2018-01-15T15:43:23Z
dc.date.issued2017
dc.identifier.issn0373-3114
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17344
dc.language.isoenen
dc.subjectFluid mechanicsen
dc.subjectKorteweg tensoren
dc.subjectGlobal existenceen
dc.subjectLong-time dynamicsen
dc.subjectScatteringen
dc.subjectSchrödinger type equationsen
dc.subject.ddc515en
dc.titleFrom Gross-Pitaevskii equation to Euler Korteweg system, existence of global strong solutions with small irrotational initial dataen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we prove the global well-posedness for small data for the Euler Korteweg system in dimension N ≥ 3, also called compressible Euler system with quantum pressure. It is formally equivalent to the Gross-Pitaevskii equation through the Madelung transform. The main feature is that our solutions have no vacuum for all time. Our construction uses in a crucial way some deep results on the scattering of the Gross-Pitaevskii equation due to Gustafson, Nakanishi and Tsai in [28, 29, 30]. An important part of the paper is devoted to explain the main technical issues of the scattering in [29] and we give a detailed proof in order to make it more accessible. Bounds for long and short times are treated with special care so that the existence of solutions does not require smallness of the initial data in H s , s > N 2 . The optimality of our assumptions is also discussed.en
dc.relation.isversionofjnlnameAnnali di Matematica Pura ed Applicata
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages40en
dc.relation.isversionofdoi10.1007/s10231-017-0702-zen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01077281en
dc.relation.isversionofjnlpublisherNicola Zanichellien
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingouien
dc.relation.forthcomingprintouien
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-15T14:40:42Z
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