Uniform controllability of a Stokes problem with a transport term in the zero-diffusion limit

Controlabilidad uniforme de un problema de Stokes con un término de transporte que cuando la difusión tiende a cero

Contrôlabilité uniforme d'un problème de Stokes avec un terme de transport quand la diffusion vaut zéro

Jon Asier Bárcena-Petisco (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper we consider a Stokes system with Navier-slip boundary conditions. The main results concern the behaviour of the cost of null controllability with respect to the diffusion coefficient when the control acts in the interior. In particular, we prove in the square that for a sufficiently large time the cost decays exponentially as the diffusion coefficient vanishes, whereas in the cube we prove that for most of the control domains and for any time T > 0 the cost explodes exponentially as the diffusion coefficient vanishes.

Mots clés: Singular limits; spectral decomposition; Stokes system; transport equation; uniform controllability

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Jon Asier Bárcena-Petisco. Uniform controllability of a Stokes problem with a transport term in the zero-diffusion limit. 2020. ⟨hal-02077608v3⟩