Null controllability of the N-dimensional Stokes system with N−1 scalar controls

In this paper we deal with the N-dimensional Stokes system in a bounded domain with Dirichlet boundary conditions. The main result establishes the null controllability with internal controls having one vanishing component. This result improves the one in [E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov, J.-P. Puel, Some controllability results for the N-dimensional Navier–Stokes and Boussinesq systems with N−1 scalar controls, SIAM J. Control Optim. 45 (1) (2006) 146–173], since no condition is imposed on the control domain.