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dc.contributor.authorSueur, Franck
dc.contributor.authorGlass, Olivier
dc.date.accessioned2012-03-14T15:12:45Z
dc.date.available2012-03-14T15:12:45Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8506
dc.language.isoenen
dc.subjectshallow-water systemen
dc.subjectCauchy problemen
dc.subjectCamassa-Holm equationsen
dc.subject.ddc515en
dc.titleSmoothness of the flow map for low-regularity solutions of the Camassa-Holm equationsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire Jacques-Louis Lions (LJLL) http://www.ann.jussieu.fr CNRS : UMR7598 – Université Paris VI - Pierre et Marie Curie;France
dc.description.abstractenIt was recently proven by De Lellis, Kappeler, and Topalov that the periodic Cauchy problem for the Camassa-Holm equations is locally well-posed in the space Lip (T) endowed with the topology of H^1 (T). We prove here that the Lagrangian flow of these solutions are analytic with respect to time and smooth with respect to the initial data. These results can be adapted to the higher-order Camassa-Holm equations describing the exponential curves of the manifold of orientation preserving diffeomorphisms of T using the Riemannian structure induced by the Sobolev inner product H^l (T), for l in N, l > 1 (the classical Camassa-Holm equation corresponds to the case l=1): the periodic Cauchy problem is locally well-posed in the space W^{2l-1,infty} (T) endowed with the topology of H^{2l-1} (T) and the Lagrangian flows of these solutions are analytic with respect to time with values in W^{2l-1,infty} (T) and smooth with respect to the initial data. These results extend some earlier results which dealt with more regular solutions. In particular our results cover the case of peakons, up to the first collision.en
dc.relation.isversionofjnlnameDiscrete and Continuous Dynamical Systems. Series A
dc.relation.isversionofjnlvol33
dc.relation.isversionofjnlissue7
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages2791-2808
dc.relation.isversionofdoihttp://dx.doi.org/10.3934/dcds.2013.33.2791
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00678729en
dc.description.sponsorshipprivatenonen
dc.relation.isversionofjnlpublisherAmerican Institute of Mathematical Sciences
dc.subject.ddclabelAnalyseen


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