  In this paper we prove an exact controllability result for the Vlasov-Stokes
system in the two-dimensional torus with small data by means of an internal
control. We show that one can steer, in arbitrarily small time, any initial
datum of class C 1 satisfying a smallness condition in certain weighted spaces
to any final state satisfying the same conditions. The proof of the main result
is achieved thanks to the return method and a Leray-Schauder fixed-point
argument.
