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The Hartree and Vlasov equations at positive density

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorSabin, Julien
dc.date.accessioned2021-12-08T09:49:10Z
dc.date.available2021-12-08T09:49:10Z
dc.date.issued2020
dc.identifier.issn0360-5302
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22334
dc.language.isoenen
dc.subjectHartree equationen
dc.subjectpositive densityen
dc.subjectsemiclassical analysisen
dc.subject.ddc520en
dc.titleThe Hartree and Vlasov equations at positive densityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider time-dependent solutions which have a finite relative energy with respect to the reference translation-invariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semi-classical limit and obtain as a by-product global well-posedness of the Vlasov equation in the (relative) energy space.en
dc.relation.isversionofjnlnameCommunications in Partial Differential Equations
dc.relation.isversionofjnlvol45en
dc.relation.isversionofjnlissue12en
dc.relation.isversionofjnldate2020-09
dc.relation.isversionofjnlpages1702-1754en
dc.relation.isversionofdoi10.1080/03605302.2020.1803355en
dc.relation.isversionofjnlpublisherTaylor & Francisen
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-12-08T09:44:19Z
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