Controllability results for cascade systems of m coupled N -dimensional stokes and Navier-stokes systems by N – 1 scalar controls

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, w...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 29; p. 31
Main Authors Takahashi, Takéo, de Teresa, Luz, Wu-Zhang, Yingying
Format Journal Article
LanguageEnglish
Published 2023
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ISSN1292-8119
1262-3377
DOI10.1051/cocv/2023014

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Summary: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2023014