Convergence to Equilibrium of a Body Moving in a Kinetic Sea

We consider a continuum of particles that are acted upon by an external force $\mathbf{G}(t,\mathbf{x})$ and that collide with a rigid body. The body itself is subject to a constant force $E$ as well as to the collective force of interaction with the particles. We assume that the particles that collide with the body reflect probabilistically with some probablility distribution $K(v,u)$. Under certain conditions on $\mathbf{G}(t,\mathbf{x})$ and $K(v,u)$, we identify an equilibrium velocity $V_{\infty }$ of the body and we prove that this equilibrium is asymptotically stable.