Stabilization of a fluid–rigid body system

We consider the mathematical model of a rigid ball moving in a viscous incompressible fluid occupying a bounded domain Ω, with an external force acting on the ball. We investigate in particular the case when the external force is what would be produced by a spring and a damper connecting the center of the ball h to a fixed point h1∈Ω. If the initial fluid velocity is sufficiently small, and the initial h is sufficiently close to h1, then we...