Motion of a rigid body in a viscous fluid

Abstract

We introduce a concept of weak solution for a boundary value problem modelling the motion of a rigid body immersedin a viscous fluid. The time variation of the fluid’s domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem.O ur main theorema ssertsth e existenceo f at least one weak solution for this problem. The result is global in time provided that the rigid body doesn ot touch the boundary.