Local null controllability of a two-dimensional fluid-structure interaction problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 1-42.

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.

DOI : https://doi.org/10.1051/cocv:2007031
Classification : 35Q30,  93C20
Mots clés : controllability, fluid-solid interaction, Navier-Stokes equations, Carleman estimates
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Boulakia, Muriel; Osses, Axel. Local null controllability of a two-dimensional fluid-structure interaction problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 1-42. doi : 10.1051/cocv:2007031. http://www.numdam.org/articles/10.1051/cocv:2007031/

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