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Uniform local null control of the Leray-α model

 

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Opened Access Uniform local null control of the Leray-α model
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Author: Dias Araruna, Fágner
Fernández Cara, Enrique
Araujo de Souza, Diego
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2014-10
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 20 (4), 1181-1202.
Document type: Article
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.
Cite: Dias Araruna, F., Fernández Cara, E. y Araujo de Souza, D. (2014). Uniform local null control of the Leray-α model. ESAIM: Control, Optimisation and Calculus of Variations, 20 (4), 1181-1202.
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URI: http://hdl.handle.net/11441/41441

DOI: 10.1051/cocv/2014011

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