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Comptes Rendus Mathématique
Volume 351, n° 13-14
pages 545-550 (juillet 2013)
Doi : 10.1016/j.crma.2013.07.019
Received : 3 May 2013 ;  accepted : 23 July 2013
A least-squares formulation for the approximation of null controls for the Stokes system
Une formulation moindres carrés de lʼapproximation de contrôles à zéro pour le système de Stokes
 

Arnaud Münch a , Pablo Pedregal b
a Laboratoire de mathématiques, Université Blaise-Pascal (Clermont-Ferrand-2), UMR CNRS 6620, campus des Cézeaux, 63177 Aubière, France 
b Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La-Mancha, 13071 Ciudad Real, Spain 

Abstract

This work deals with the approximation of distributed null controls for the Stokes equation. The existence of   controls has been obtained by Fursikov and Imanuvilov (1996) [[5]] via Carleman-type estimates. We introduce and analyze a least-squares formulation of the controllability problem, and we show that it allows the construction of convergent sequences of functions toward null controls for the Stokes system.

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Résumé

Cette note concerne lʼapproximation de contrôles exactes pour le système de Stokes. Lʼexistence de contrôles   a été obtenue dans Fursikov et Imanuvilov (1996) [[5]], en utilisant des inégalités de type Carleman. On introduit et analyse une formulation de type moindres carrés et on montre quʼelle permet la construction de suites convergentes de fonctions vers des contrôles à zéro du système de Stokes.

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