| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 31 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2023014 | |
| 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*,**
1
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: ldeteresa@im.unam.mx
Received:
14
April
2022
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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