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Article Dans Une Revue Journal of Evolution Equations Année : 2024

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

Résumé

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 et versions

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

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Takéo Takahashi, Luz de Teresa, Yingying Wu-Zhang. A Kalman condition for the controllability of a coupled system of Stokes equations. Journal of Evolution Equations, 2024, ⟨10.1007/s00028-023-00935-6⟩. ⟨hal-03936869v2⟩
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