Locally distributed control for a model of fluid-structure interaction

We consider the equations modeling the coupled vibrations of a fluid-solid system. The control acts in a subset of a domain occupied by the fluid. Our main result asserts that we have exact controllability and exponential stabilizability provided that the support of the control contains a neighborhood of the solid and a neighborhood of the exterior boundary. This improves the existing exact controllability results, which require a control which is active in the whole fluid domain. The proof is based on a frequency domain approach, combined with the use of appropriate multipliers. Moreover, we show that the strong stabilizability property holds for any open control region.