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The existence of weak solutions to the "viscous incompressible fluid + rigidbody" system with Navier slip-with-friction conditions in a 3D bounded domainhas been recently proved by G\'{e}rard-Varet and Hillairet in \cite{exi:GeH}.In 2D for a fluid alone (without any rigid body) it is well-known since Leraythat weak solutions are unique, continuous in time with $ L^{2} $ regularity inspace and satisfy the energy equality.In this paper we prove that theseproperties also hold for the 2D "viscous incompressible fluid + rigid body"system.

On the weak uniqueness of "viscous incompressible fluid + rigid body" system with Navier slip-with-friction conditions in a 2D bounded domain