Local null controllability of a two-dimensional fluid-structure interaction problem

Muriel Boulakia (1) , Axel Osses (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DIMEC - Departamento de Ingeniería Mecánica

In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given T > 0, the system can be driven at rest and the structure to its reference configuration at time T. To show this result, we first consider a linearized system. Thanks to an observability inequality obtained from a Carleman inequality, we prove an optimal controllability result with a regular control. Next, with the help of Kakutani's fixed point theorem and a regularity result, we pass to the nonlinear problem.

Domaines: Equations aux dérivées partielles [math.AP]

Muriel Boulakia, Axel Osses. Local null controllability of a two-dimensional fluid-structure interaction problem. [Research Report] 2007. ⟨inria-00542535⟩