Controllability results for cascade systems of $m$ coupled $N$-dimensional Stokes and Navier-Stokes systems by $N−1$ scalar controls - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2023

Controllability results for cascade systems of $m$ coupled $N$-dimensional Stokes and Navier-Stokes systems by $N−1$ scalar controls

Résumé

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 $m \times N$ state (corresponding to the velocities of the fluids) by $N−1$ distributed scalar controls. The proof of the controllability of the coupled Stokes system 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.
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Dates et versions

hal-03325287 , version 1 (24-08-2021)

Identifiants

Citer

Takéo Takahashi, Luz de Teresa, Ying Wu-Zhang. Controllability results for cascade systems of $m$ coupled $N$-dimensional Stokes and Navier-Stokes systems by $N−1$ scalar controls. ESAIM: Control, Optimisation and Calculus of Variations, 2023, ⟨10.48550/arXiv.2108.09856⟩. ⟨hal-03325287⟩
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