Controllability results for cascade systems of m coupled N -dimensional stokes and Navier-stokes systems by N – 1 scalar controls - Takahashi, Takéo; de Teresa, Luz; Wu-Zhang, Yingying (ESAIM. Control, optimisation and calculus of variations, 2023)
In this paper we deal with the controllability properties of a system of m coupled Stokes systems or m coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, we impose that this control has a vanishing component so that we control a m × N state (corresponding to the velocities of the fluids) by N — 1 distributed scalar controls. The proof of the controllability of the coupled Stokes systems is based on a Carleman estimate for the adjoint system. The local null-controllability of the coupled Navier-Stokes systems is then obtained by means of the source term method and a Banach fixed point.