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In this paper we study the motion of a rigid body driven by Newton's lawimmersed in a stationary incompressible Stokes flow occupying a bounded simplyconnected domain. The aim is that of trajectory tracking of the solid by themeans of a control in the form of Dirichlet boundary data on the outsideboundary of the fluid domain. We show that it is possible to exactly achieveany smooth trajectory for the solid that stays away from the external boundary,by the means of such a remote control. The proof relies on some density methodsfor the Stokes system, as well as a reformulation of the solid equations intoan ODE.

Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number