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

Abstract : 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.
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https://hal.inria.fr/inria-00542535
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Submitted on : Thursday, December 2, 2010 - 9:19:52 PM
Last modification on : Sunday, June 26, 2022 - 5:21:27 AM
Long-term archiving on: : Thursday, March 3, 2011 - 3:05:43 AM

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  • HAL Id : inria-00542535, version 1

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

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