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The aim of this work is to show the local null controllability of afluid-solid interaction system by using a distributed control located in thefluid. The fluid is modeled by the incompressible Navier-Stokes system withNavier slip boundary conditions and the rigid body is governed by the Newtonlaws. Our main result yields that we can drive the velocities of the fluid andof the structure to 0 and we can control exactly the position of the rigidbody. One important ingredient consists in a new Carleman estimate for a linearfluid-rigid body system with Navier boundary conditions. This work is donewithout imposing any geometrical conditions on the rigid body.

Local null controllability of a fluid-rigid body interaction problem with Navier slip boundary conditions