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

publié le

Edoardo Bocchi
(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 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)