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

2021/08/22 by Takéo Takahashi, Takahashi, Takéo, Luz de Teresa +3
Computer Science · Engineering · Mathematics · #35Q30 #76D05 #93B05 #93B07 #93C10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.09856

openalex publication_date 2021/08/22 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

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 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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