no. 4
Uniform local null control of the Leray-α model
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1181-1202.

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.

DOI : 10.1051/cocv/2014011
Classification : 93B05, 35Q35, 35G25, 93B07
Mots clés : null controllability, Carleman inequalities, Leray-αmodel, Navier−Stokes equations 
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     title = {Uniform local null control of the {Leray-}$\alpha $ model},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1181--1202},
     publisher = {EDP-Sciences},
     volume = {20},
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     year = {2014},
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     zbl = {1297.93031},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2014011/}
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Araruna, Fágner D.; Fernández-Cara, Enrique; Souza, Diego A. Uniform local null control of the Leray-$\alpha $ model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1181-1202. doi : 10.1051/cocv/2014011. http://www.numdam.org/articles/10.1051/cocv/2014011/

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