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Exact controllability of a fluid-rigid body system

Oleg Imanuvilov 1 Takéo Takahashi 2, 3 
3 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : This paper is devoted to the controllability of a 2D fluid-structure system. The fluid is viscous and incompressible and its motion is modelled by the Navier-Stokes equations whereas the structure is a rigid ball which satisfies Newton's laws. We prove the local null controllability for the velocities of the fluid and of the rigid body and the exact controllability for the position of the rigid body. An important part of the proof relies on a new Carleman inequality for an auxiliary linear system coupling the Stokes equations with some ordinary differential equations.
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https://hal.archives-ouvertes.fr/hal-00590648
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Submitted on : Wednesday, May 4, 2011 - 2:23:10 PM
Last modification on : Saturday, June 25, 2022 - 7:41:40 PM

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Oleg Imanuvilov, Takéo Takahashi. Exact controllability of a fluid-rigid body system. Journal de Mathématiques Pures et Appliquées, Elsevier, 2007, 87 (4), pp.408-437. ⟨10.1016/j.matpur.2007.01.005⟩. ⟨hal-00590648⟩

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