The local existence of strong solutions for the interaction of a rigid disk with a two-dimensional viscous incompressible flow is studied in [C. Grandmont and Y. Maday, C. R. Acad. Sci. Paris, Sér. I, Math. 326, No. 4, 525-530 (1998; Zbl 0924.76022)]. In the present paper, a global weak formulation of the above problem is introduced, for a finite number of rigid bodies in interaction with an incompressible viscous fluid, in a bounded domain with dimension 2 or 3. The existence of solutions for a particular form of the initial velocities is proved. In the absence of collisions, a global in time solution exists in the plane; in dimension 3 it is necessary to have small enough data. The main part of the proof involves the Di Perna-Lions theorem on compactness of sequences of solutions to linear transport equations.