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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorALVAREZ-SAMANIEGO, Borys
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
dc.date.accessioned2024-04-04T03:15:43Z
dc.date.available2024-04-04T03:15:43Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194164
dc.description.abstractEnWe study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations.
dc.language.isoen
dc.title.enA Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxivmath.AP/0701681
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00126256
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00126256v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ALVAREZ-SAMANIEGO,%20Borys&LANNES,%20David&rft.genre=preprint


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