Controllability results for cascade systems of $m$ coupled $N$-dimensional Stokes and Navier-Stokes systems by $N-1$ scalar controls
Analysis of PDEs
2022-04-13 v2
Abstract
In this paper, we deal with the controllability properties of a system of coupled Stokes systems or 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 state (corresponding to the velocities of the fluids) by 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.
Keywords
Cite
@article{arxiv.2108.09856,
title = {Controllability results for cascade systems of $m$ coupled $N$-dimensional Stokes and Navier-Stokes systems by $N-1$ scalar controls},
author = {Takéo Takahashi and Luz de Teresa and Ying Wu-Zhang},
journal= {arXiv preprint arXiv:2108.09856},
year = {2022}
}