A Kalman condition for the controllability of a coupled system of Stokes equations - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2023

A Kalman condition for the controllability of a coupled system of Stokes equations

Abstract

We consider the controllability of a class of systems of n Stokes equations, coupled through terms of order zero and controlled by m distributed controls. Our main result states that such a system is null-controllable if and only if a Kalman type condition is satisfied. This generalizes the case of finite-dimensional systems and the case of systems of coupled linear heat equations. The proof of the main result relies on the use of the Kalman operator introduced in [1] and on a Carleman estimate for a cascade type system of Stokes equations. Using a fixed-point argument, we also obtain that if the Kalman condition is verified, then the corresponding system of Navier-Stokes equations is locally null-controllable.
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Dates and versions

hal-03936869 , version 1 (12-01-2023)
hal-03936869 , version 2 (20-09-2023)

Identifiers

  • HAL Id : hal-03936869 , version 1

Cite

Takéo Takahashi, Luz de Teresa, Yingying Wang. A Kalman condition for the controllability of a coupled system of Stokes equations. 2023. ⟨hal-03936869v1⟩

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