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WAVES INTERACTING WITH A PARTIALLY IMMERSED OBSTACLE IN THE BOUSSINESQ REGIME

hal.structure.identifierLaboratoire de Mathématiques [LAMA]
dc.contributor.authorBRESCH, D.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
dc.date.accessioned2024-04-04T03:02:09Z
dc.date.available2024-04-04T03:02:09Z
dc.date.issued2021
dc.identifier.issn2157-5045
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192954
dc.description.abstractEnThis paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in dimension d= 1 for 2 × 2 hyperbolic systems are well understood. However, for many applications, and especially for the description of surface water waves, dispersive perturbations of hyperbolic systems must be considered. We consider here a configuration where the motion of the waves is governed by a Boussinesq system (a dispersive perturbation of the hyperbolic nonlinear shallow water equations), and in the presence of a fixed partially immersed obstacle. We shall insist on the differences and similarities with respect to the standard hyperbolic case, and focus our attention on a new phenomenon, namely, the apparition of a dispersive boundary layer. In order to obtain existence and uniform bounds on the solutions over the relevant time scale, a control of this dispersive boundary layer and of the oscillations in time it generates is necessary. This analysis leads to a new notion of compatibility condition that is shown to coincide with the standard hyperbolic compatibility conditions when the dispersive parameter is set to zero. To the authors' knowledge, this is the first time that these phenomena (likely to play a central role in the analysis of initial boundary value problems for dispersive perturbations of hyperbolic systems) are exhibited.
dc.description.sponsorshipFrontières numériques et couplages - ANR-17-CE40-0025
dc.description.sponsorshipEcoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.subject.enTransmission problem
dc.subject.enFree surface
dc.subject.enBoussinesq system
dc.subject.enWave-structure interaction
dc.subject.enDispersive boundary layer
dc.subject.enOscillations in time
dc.subject.enLocal well posedness
dc.subject.enCompatibility conditions
dc.title.enWAVES INTERACTING WITH A PARTIALLY IMMERSED OBSTACLE IN THE BOUSSINESQ REGIME
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.identifier.arxiv1902.04837
bordeaux.journalAnalysis & PDE
bordeaux.page1085–1124
bordeaux.volume14
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02015531
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02015531v1
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