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dc.contributor.authorGallouët, Thomas*
dc.contributor.authorNatale, Andrea*
dc.contributor.authorVialard, François-Xavier*
dc.date.accessioned2019-12-18T09:28:48Z
dc.date.available2019-12-18T09:28:48Z
dc.date.issued2020
dc.identifier.issn0003-9527
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20333
dc.language.isoenen
dc.subjectgeodesic problem
dc.subjectfluid flows
dc.subject.ddc515en
dc.titleGeneralized compressible flows and solutions of the H(div) geodesic problem
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the geodesic problem on the group of diffeomorphism of a domain M⊂Rd, equipped with the H(div) metric. The geodesic equations coincide with the Camassa-Holm equation when d=1, and represent one of its possible multi-dimensional generalizations when d>1. We propose a relaxation à la Brenier of this problem, in which solutions are represented as probability measures on the space of continuous paths on the cone over M. We use this relaxation to prove that smooth H(div) geodesics are globally length minimizing for short times. We also prove that there exists a unique pressure field associated to solutions of our relaxation. Finally, we propose a numerical scheme to construct generalized solutions on the cone and present some numerical results illustrating the relation between the generalized Camassa-Holm and incompressible Euler solutions.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlissue235
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages1707–1762
dc.relation.isversionofdoi10.1007/s00205-019-01453-x
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-04-27T08:53:24Z
hal.person.labIds60*
hal.person.labIds60*
hal.person.labIds1001627$$$60*


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