The motion of a rigid body and a viscous fuid in abounded domain in presence of collisions

Abstract

We consider the motion of a rigid body in a bounded domain filled by viscous incompressible fluid. The fluid is described by the Navier-Stokes equations. We assume the Navier condition on the boundary of the body and the Dirichlet condition on the boundary of the domain. We give the global-in-time solvability result of the weak solution. The result allows a possibility of collisions of the body with the boundary of the domain.