2018/02/21 by Edoardo Bocchi, Bocchi, Edoardo · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.1802.07643
openalex publication_date 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.