  In this article, we study the long-time behavior of solutions of the
two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by
the two-dimensional Navier-Stokes equations, and the disk moves under the
influence of the forces exerted by the viscous fluid. We first derive
$L^p$-$L^q$ decay estimates for the linearized equations and compute the first
term in the asymptotic expansion of the solutions of the linearized equations.
We then apply these computations to derive time-decay estimates for the
solutions to the full Navier-Stokes fluid-rigid disk system.
