Floating structures in shallow water: local well-posedness in the axisymmetric case
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BOCCHI, Edoardo | |
| dc.date.accessioned | 2024-04-04T02:59:36Z | |
| dc.date.available | 2024-04-04T02:59:36Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192753 | |
| dc.description.abstractEn | The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of two evolution equations on the surface elevation and the horizontal discharge. The presence of the object is accounted for by a constraint on the discharge under the object; the pressure exerted by the fluid on this object is then the Lagrange multiplier associated to this constraint. Our goal in this paper is to prove the well-posedness of this fluid-structure interaction problem in the shallow water approximation under the assumption that the flow is axisymmetric without swirl. We write the fluid equations as a quasilinear hyperbolic mixed initial boundary value problem and the solid equation as a second order ODE coupled to the fluid equations. Finally we prove the local in time well-posedness for this coupled problem, provided some compatibility conditions on the initial data are satisfied. | |
| dc.language.iso | en | |
| dc.title.en | Floating structures in shallow water: local well-posedness in the axisymmetric case | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Physique [physics]/Physique [physics]/Physique Atmosphérique et Océanique [physics.ao-ph] | |
| dc.subject.hal | Physique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph] | |
| dc.subject.hal | Physique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn] | |
| dc.identifier.arxiv | 1802.07643 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01714437 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01714437v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BOCCHI,%20Edoardo&rft.genre=preprint |
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