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

Abstract

We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of ℝd (d = 2 or 3) with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence of solutions for initial velocities in H10 (Ω). In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions is infinite only for small enough data.