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In this paper, we consider two systems modelling the evolution of a rigidbody in an incompressible fluid in a bounded domain of the plane. The firstsystem corresponds to an inviscid fluid driven by the Euler equation whereasthe other one corresponds to a viscous fluid driven by the Navier-Stokessystem. In both cases we investigate the uniqueness of weak solutions, "\`a laYudovich" for the Euler case, "\`a la Leray" for the Navier-Stokes case, aslong as no collision occurs.

Uniqueness results for weak solutions of two-dimensional fluid-solid systems