Stabilization of a rigid body moving in a compressible viscous fluid

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 h 1 . 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 h 1 . 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 h 1 as t → ∞ .