Volume 14, Number 1, January-March 2008
|Page(s)||1 - 42|
|Published online||20 July 2007|
Local null controllability of a two-dimensional fluid-structure interaction problem
Laboratoire de Mathématiques Appliquées, Université de
Versailles-St-Quentin, 45 avenue des États-Unis, 78035 Versailles
Cedex, France; email@example.com
2 Departamento de Ingenería Matemática and Centro de Modelamiento Matemático UMI 2807 CNRS, Facultad de Ciencias de Físicas y Matemáticas, Universidad de Chile, Casilla 170/3 - Correo 3, Santiago, Chile; firstname.lastname@example.org
Revised: 5 April 2006
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.
Mathematics Subject Classification: 35Q30 / 93C20
Key words: Controllability / fluid-solid interaction / Navier-Stokes equations / Carleman estimates
© EDP Sciences, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.