Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
Résumé
In this paper, we prove a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain of R^3 with null Dirichlet boundary conditions. The control is distributed into an (arbitrarily small) open subset and has two vanishing components. J.-L. Lions and E. Zuazua proved that the linearized system is not necessarily approximately controllable even if the control is distributed on the entire domain, hence it cannot be null controllable and the standard linearization method fails. We use the return method together with a new algebraic method inspired by the works of M.Gromov and previous results by M.Gueye.
Domaines
Optimisation et contrôle [math.OC]
Origine : Fichiers produits par l'(les) auteur(s)