Volume 29, 2023
|Number of page(s)||24|
|Published online||28 April 2023|
Controllability Results for Cascade Systems of m Coupled N-Dimensional Stokes and Navier-Stokes Systems by N – 1 Scalar Controls*,**
Université de Lorraine, CNRS, Inria, IECL, 54000 Nancy, France
2 Instituto de Matematicas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., C. P. 04510 Ciudad de México, Mexico
*** Corresponding author: firstname.lastname@example.org
Accepted: 5 March 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.
Mathematics Subject Classification: 76D05 / 35Q30 / 93B05 / 93B07 / 93C10
Key words: Null controllability / Navier-Stokes systems / Carleman estimates
© The authors. Published by EDP Sciences, SMAI 2023
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