Stabilization of a fluid-rigid body system
The authors consider the motion of a rigid ball inside an incompressible viscous fluid occupying a domain \(\Omega\subset \mathbb R^3\). An external force is acting on the ball as a spring, with additional damping, connecting the center \(h(t)\) of the ball to a fixed point \(h_1\in\Omega\). They prove that if the initial velocity of the fluid is small together with the distance \(\|h(t)-h_1\|\), the model admits a global unique solution. They finally study related control problems associated to the feedback associated to \(h\).
scientific article; zbMATH DE number 6484244