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WELL-POSEDNESS AND SHALLOW-WATER STABILITY FOR A NEW HAMILTONIAN FORMULATION OF THE WATER WAVES EQUATIONS WITH VORTICITY

hal.structure.identifierInstituto de Ciencias Matematicas [ICMAT]
dc.contributor.authorCASTRO, Angel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
dc.date.accessioned2024-04-04T03:19:45Z
dc.date.available2024-04-04T03:19:45Z
dc.date.issued2015
dc.identifier.issn0022-2518
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194535
dc.description.abstractEnIn this paper we derive a new formulation of the water waves equa-tions with vorticity that generalizes the well-known Zakharov-Craig-Sulem for-mulation used in the irrotational case. We prove the local well-posedness of this formulation, and show that it is formally Hamiltonian. This new formu-lation is cast in Eulerian variables, and in finite depth; we show that it can be used to provide uniform bounds on the lifespan and on the norms of the solutions in the singular shallow water regime. As an application to these re-sults, we derive and provide the first rigorous justification of a shallow water model for water waves in presence of vorticity; we show in particular that a third equation must be added to the standard model to recover the velocity at the surface from the averaged velocity. The estimates of the present paper also justify the formal computations of [15] where higher order shallow water models with vorticity (of Green-Naghdi type) are derived.
dc.description.sponsorshipDYnamique des Fluides, Couches Limites, Tourbillons et Interfaces - ANR-13-BS01-0003
dc.description.sponsorshipFrontières, numérique, dispersion. - ANR-13-BS01-0009
dc.language.isoen
dc.publisherIndiana University Mathematics Journal
dc.title.enWELL-POSEDNESS AND SHALLOW-WATER STABILITY FOR A NEW HAMILTONIAN FORMULATION OF THE WATER WAVES EQUATIONS WITH VORTICITY
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalIndiana University Mathematics Journal
bordeaux.page1169-1270
bordeaux.volume64
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01101988
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01101988v1
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