  We study in this paper the movement of a rigid solid inside an incompressible
Navier-Stokes flow, within a bounded domain. We consider the case where slip is
allowed at the fluid/solid interface, through a Navier condition. Taking into
account slip at the interface is very natural within this model, as classical
no-slip conditions lead to unrealistic collisional behavior between the solid
and the domain boundary. We prove for this model existence of weak solutions of
Leray type, up to collision, in three dimensions. The key point is that, due to
the slip condition, the velocity field is discontinuous across the fluid/solid
interface. This prevents from obtaining global H1 bounds on the velocity, which
makes many aspects of the theory of weak solutions for Dirichlet conditions
unadapted.
