On the controllability of the 2-D Vlasov-Stokes system

Abstract

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.