Problem on a drift of a rigid body in a viscous fluid

The work is devoted to the investigation of the problem about the inertia-free motion of a rigid body in a viscous incompressible fluid whose flow is governed by the Stokes equations. The following result is proved: if initially the body does not touch the boundary of the flow domain, then the problem has a unique generalized solution up to the instant of the first collision of the body with the boundary. The uniqueness of the solution is the main outcome of the paper. Besides that, new results about operators and function spaces being related to the problem are obtained.