A least-squares formulation for the approximation of null controls for the Stokes system

Arnaud Munch (1) , Pablo Pedregal (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 E.T.S. Ingenieros Industriales

This note deals with the approximation of distributed null controls for the Stokes equation. The existence of $L^2$ controls have been obtained in \textit{[Fursikov \& Imanuvilov, Controllability of Evolution Equations, 1996])} 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.

Mots clés: Stokes system; Null controllability; Approximation; least-squares

Domaines: Optimisation et contrôle [math.OC]

Arnaud Munch, Pablo Pedregal. A least-squares formulation for the approximation of null controls for the Stokes system. 2013. ⟨hal-00819426v3⟩