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

Abstract

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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.

How to cite

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Araruna, 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 -

References

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