Stabilization of a rigid body moving in a compressible viscous fluid

Arnab Roy (1, 2) , Takéo Takahashi (1, 2)

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

We consider the stabilizability of a fluid-structure interaction system where the fluid is viscous and compressible and the structure is a rigid ball. The feedback control of the system acts on the ball and corresponds to a force that would be produced by a spring and a damper connecting the center of the ball to a fixed point h1. We prove the global-in-time existence of strong solutions for the corresponding system under a smallness condition on the initial velocities and on the distance between the initial position of the center of the ball and h1. Then, we show with our feedback law, that the fluid and the structure velocities go to 0 and that the center of the ball goes to $h1$ as $t → ∞$.

Mots clés: Fluid-structure interaction; global solutions; compressible Navier-Stokes system; stabilization

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Arnab Roy, Takéo Takahashi. Stabilization of a rigid body moving in a compressible viscous fluid. Journal of Evolution Equations, 2021, ⟨10.1007/s00028-020-00574-1⟩. ⟨hal-02314870⟩