On the existence of strong solutions to a fluid structure interaction problem with Navier boundary conditions

Imene A Djebour (1, 2) , Takéo Takahashi (1, 2)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine

We consider a fluid-structure interaction system composed by a three-dimensional viscous incompressible fluid and an elastic plate located on the upper part of the fluid boundary. The fluid motion is governed by the Navier-Stokes system whereas we add a damping in the plate equation. We use here Navier-slip boundary conditions instead of the standard no-slip boundary conditions. The main results are the local in time existence and uniqueness of strong solutions of the corresponding system and the global in time existence and uniqueness of strong solutions for small data and if we assume the presence of frictions in the boundary conditions.

Mots clés: damped beam equation; strong solutions; Navier-Stokes system; fluid-structure interaction systems

Domaines: Equations aux dérivées partielles [math.AP]

Imene A Djebour, Takéo Takahashi. On the existence of strong solutions to a fluid structure interaction problem with Navier boundary conditions. Journal of Mathematical Fluid Mechanics, 2019, 21, pp.36. ⟨10.1007/s00021-019-0440-7⟩. ⟨hal-02061542⟩