Non-uniqueness of the solution to the problem of a motion of a rigid body in a viscous incompressible fluid

This paper is devoted to the investigation of the problem on a motion of a rigid body in a viscous incompressible fluid. It is proved that there exist at least two weak solutions of this problem, if the collisions of the body with the boundary of the flow domain are allowed. These solutions have different behavior of the body after the collision. Namely, for the first solution, the body goes away from the boundary after the collision. In the second solution, the body and the boundary remain in contact.