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

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.