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navier−stokes equations

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Uniform local null control of the Leray-α model ∗∗∗
Fágner D. Araruna, Enrique Fernández-Cara, Diego A. Souza
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 4 / October 2014

Published online by Cambridge University Press:

08 August 2014, pp. 1181-1202

Print publication:

October 2014
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This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc.