# Uniform local null control of the Leray-α model

Fágner D. Araruna; Enrique Fernández-Cara; Diego A. Souza

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 1181-1202
- ISSN: 1292-8119

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topAraruna, Fágner D., Fernández-Cara, Enrique, and Souza, Diego A.. "Uniform local null control of the Leray-α model." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 1181-1202. <http://eudml.org/doc/272808>.

@article{Araruna2014,

abstract = {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.},

author = {Araruna, Fágner D., Fernández-Cara, Enrique, Souza, Diego A.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {null controllability; Carleman inequalities; Leray-αmodel; Navier−Stokes equations; Leray- model; Navier-Stokes equations},

language = {eng},

number = {4},

pages = {1181-1202},

publisher = {EDP-Sciences},

title = {Uniform local null control of the Leray-α model},

url = {http://eudml.org/doc/272808},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Araruna, Fágner D.

AU - Fernández-Cara, Enrique

AU - Souza, Diego A.

TI - Uniform local null control of the Leray-α model

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 4

SP - 1181

EP - 1202

AB - 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.

LA - eng

KW - null controllability; Carleman inequalities; Leray-αmodel; Navier−Stokes equations; Leray- model; Navier-Stokes equations

UR - http://eudml.org/doc/272808

ER -

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