Existence of weak solutions for the motion of rigid bodies in a viscous uid

We study the evolution of a nite number of rigid bodies within a viscous incompressible uid in a bounded domain of IR d (d = 2 or 3) with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence of solutions for H 1 0 ( ) initial velocities. In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions is in nite only for small enough data. AMS Subject Classi cation: 35Q10, 76D99, 73B99.