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Generalized solutions for the Euler equations in one and two dimensions

dc.contributor.authorBernot, Marc
dc.contributor.authorFigalli, Alessio
dc.contributor.authorSantambrogio, Filippo
dc.date.accessioned2009-07-03T08:09:25Z
dc.date.available2009-07-03T08:09:25Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/717
dc.language.isoenen
dc.subjectEuler incompressibleen
dc.subject.ddc519en
dc.titleGeneralized solutions for the Euler equations in one and two dimensionsen
dc.typeArticle accepté pour publication ou publiéen_US
dc.contributor.editoruniversityotherUniversité de Nice Sophia-Antipolis;France
dc.contributor.editoruniversityotherEcole Normale Supérieure de Lyon;France
dc.description.abstractenIn this paper we study generalized solutions (in the Brenier's sense) for the Euler equations. We prove that uniqueness holds in dimension one whenever the pressure field is smooth, while we show that in dimension two uniqueness is far from being true. In the case of the two-dimensional disc we study solutions to Euler equations where particles located at a point $x$ go to $-x$ in a time $\pi$, and we give a quite general description of the (large) set of such solutions. As a byproduct, we can construct a new class of classical solutions to Euler equations in the disc.en
dc.relation.isversionofjnlnameJournal de Mathématiques Pures et Appliquées
dc.relation.isversionofjnlvol91en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2009-02
dc.relation.isversionofjnlpages137-155en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.matpur.2008.09.011en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00284725/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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