Analysis of a simplified model of rigid structure floating in a viscous fluid
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAITY, Debayan | |
| hal.structure.identifier | Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] [CMM] | |
| dc.contributor.author | SAN MARTIN, Jorge | |
| hal.structure.identifier | Institut Élie Cartan de Lorraine [IECL] | |
| hal.structure.identifier | Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX] | |
| dc.contributor.author | TAKAHASHI, Takéo | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TUCSNAK, Marius | |
| dc.date.accessioned | 2024-04-04T03:04:59Z | |
| dc.date.available | 2024-04-04T03:04:59Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0938-8974 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193204 | |
| dc.description.abstractEn | We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we propose a new model for this interaction, taking into consideration the viscosity of the fluid. This is done supposing that the flow obeys a shallow water regime (modeled by the viscous Saint-Venant equations in one space dimension) and using a Hamiltonian formalism. Another contribution of this work is establishing the well-posedness of the obtained PDEs/ODEs system in function spaces similar to the standard ones for strong solutions of viscous shallow water equations. Our well-posedness results are local in time for every initial data and global in time if the initial data are close (in appropriate norms) to an equilibrium state. Moreover, we show that the linearization of our system around an equilibrium state can be described, at least for some initial data, by an integro-fractional differential equation related to the classical Cummins equation and which reduces to the Cummins equation when the viscosity vanishes and the fluid is supposed to fill the whole space. Finally, we describe some numerical tests, performed on the original nonlinear system, which illustrate the return to equilibrium and the influence of the viscosity coefficient. | |
| dc.description.sponsorship | Systèmes interconnectés de dimension infinie pour les milieux hétérogènes - ANR-16-CE92-0028 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Viscous shallow water equations | |
| dc.subject.en | floating structure | |
| dc.subject.en | strong solutions | |
| dc.subject.en | fluid-structure interaction | |
| dc.subject.en | return to equilibrium | |
| dc.title.en | Analysis of a simplified model of rigid structure floating in a viscous fluid | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00332-019-09536-5 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Nonlinear Science | |
| bordeaux.page | 1975–2020 | |
| bordeaux.volume | 29 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01889892 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01889892v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Nonlinear%20Science&rft.date=2019&rft.volume=29&rft.issue=5&rft.spage=1975%E2%80%932020&rft.epage=1975%E2%80%932020&rft.eissn=0938-8974&rft.issn=0938-8974&rft.au=MAITY,%20Debayan&SAN%20MARTIN,%20Jorge&TAKAHASHI,%20Tak%C3%A9o&TUCSNAK,%20Marius&rft.genre=article |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||