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

Imene A Djebour (1)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

The aim of this work is to show the local null controllability of a fluid-solid interaction system by using a distributed control located in the fluid. The fluid is modeled by the incompressible Navier-Stokes system with Navier slip boundary conditions and the rigid body is governed by the Newton laws. Our main result yields that we can drive the velocities of the fluid and of the structure to 0 and we can control exactly the position of the rigid body, provided that its shape is not a disk. One important ingredient consists in a new Carleman estimate for a linear fluid-rigid body system with Navier boundary conditions.

Domaines: Mathématiques [math]

Imene A Djebour. Local null controllability of a fluid-rigid body interaction problem with Navier slip boundary conditions. 2020. ⟨hal-02454567v1⟩