Local null controllability of a fluid-solid interaction problem in dimension 3

Muriel Boulakia (1, 2) , Sergio Guerrero (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows

We are interested by the three-dimensional coupling between an incompressible fluid and a rigid body. The fluid is modeled by the Navier-Stokes equations, while the solid satisfies the Newton's laws. In the main result of the paper we prove that, with the help of a distributed control, we can drive the fluid and structure velocities to zero and the solid to a reference position provided that the initial velocities are small enough and the initial position of the structure is close to the reference position. This is done without any condition on the geometry of the rigid body.

Domaines: Equations aux dérivées partielles [math.AP]

Muriel Boulakia, Sergio Guerrero. Local null controllability of a fluid-solid interaction problem in dimension 3. Journal of the European Mathematical Society, 2013, 15 (3), pp.825-856. ⟨hal-00847963⟩