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

We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of R-d (d = 2 or 3) With Dirichlet boundary conditions. By introducing an appropriate weak formulation for th e complete problem we prove existence of solutions for initial velocities i n H-0(1)(Ohm). In the absence of collisions, solutions exist for all time i n dimension 2, whereas in dimension 3 the lifespan of solutions is infinite only for small enough data.