| Issue |
ESAIM: COCV
Volume 20, Number 4, October-December 2014
|
|
|---|---|---|
| Page(s) | 1181 - 1202 | |
| DOI | https://doi.org/10.1051/cocv/2014011 | |
| Published online | 08 August 2014 | |
Uniform local null control of the Leray-α model∗,∗∗
1
Departamento de Matemática, Universidade Federal da
Paraíba, 58051-900
João Pessoa
PB,
Brasil
fagner@mat.ufpb.br
2 Departamento EDAN, University of Sevilla, Aptdo. 1160, 41080
Sevilla, Spain
cara@us.es; desouza@us.es
Received: 22 November 2013
Revised: 8 February 2014
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.
Mathematics Subject Classification: 93B05 / 35Q35 / 35G25 / 93B07
Key words: Null controllability / Carleman inequalities / Leray-αmodel / Navier−Stokes equations
© EDP Sciences, SMAI, 2014
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