## Séminaires doctorant

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Plan d’accès

Le séminaire doctorant a lieu le vendredi à 15h15 en salle 324-2B.

Responsables :
Isabelle Baraquin, Lucie Delcey

### Exposés à venir

Vendredi 27 avril 2018 : Horaire inhabituel : 13h30-14h30
Edoardo Bocchi
(Institut de Mathématiques de Bordeaux)

Floating structures in shallow water : local well-posedness in the axisymmetric case.

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 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 with this constraint. Our goal 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.

References :
[1] E. BOCCHI, Floating structures in shallow water : local well-posedness in the axisymmetric case, arXiv preprint (2018)

### Archives

Vendredi 10 novembre 2017 : Lucie Delcey (LMB) Stabilité spectrale pour l’équation de Lugiato-Lefever

Vendredi 24 novembre 2017 : Gunjan Sapra (Kyoto University) Decomposability and 2-positivity of linear map from $M_3(\mathbb{C})$ to $M_9(\mathbb{C})$

Vendredi 15 décembre 2017 : Sushma Kumari (Kyoto university) Universal consistency of k-NN rule in $\sigma$-finite dimensional metric spaces

Vendredi 12 janvier 2018 : Adnan Alahmad (LMB) Numerical zoom model multiscale problems with small defects

Vendredi 2 février 2018 : Quentin Fortier (Lycée Victor Hugo) Connexité avec contraintes de matroïdes dans les graphes

Vendredi 9 février 2018 : Olga Gorynina (LMB) Time and space adaptivity for wave equation

Vendredi 9 mars 2018 : Antonio J. Fernández (LMB & LAMAV (Univ. Valenciennes)) Elliptic PDE : from linear to fully nonlinear via some relevant examples

Mardi 20 mars 2018 : Marine Rougnant (LMB) Études statistiques autour d’une conjecture de Gras sur la p-rationalité

Archives 2016/2017

## Agenda

• ### Vendredi 27 avril 13:30-14:30 - Edoardo Bocchi - Institut de Mathématiques de Bordeaux

Séminaire doctorant : Floating structures in shallow water : local well-posedness in the axisymmetric case.

Résumé :
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 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 with this constraint. Our goal 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.
References :
[1] E. BOCCHI, Floating structures in shallow water : local well-posedness in the axisymmetric case, arXiv preprint (2018)