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

Edoardo Bocchi (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]

Edoardo Bocchi. Floating structures in shallow water: local well-posedness in the axisymmetric case. 2019. ⟨hal-01714437v3⟩