  We consider a single disk moving under the influence of a 2D viscous fluid
and we study the asymptotic as the size of the solid tends to zero.If the
density of the solid is independent of $\varepsilon$, the energy equality is
not sufficient to obtain a uniform estimate for the solid velocity. This will
be achieved thanks to the optimal $L^p-L^q$ decay estimates of the semigroup
associated to the fluid-rigid body system and to a fixed point argument. Next,
we will deduce the convergence to the solution of the Navier-Stokes equations
in $\R^2$.
