Uniform local null control of the Leray-α model∗∗∗. (8th August 2014)

• Record Type: Journal Article
• Authors: Araruna, Fágner D.; Fernández-Cara, Enrique; Souza, Diego A.
• Is Part Of: ESAIM. Volume 20:Number 4(2014:Oct.)
• Page Start: 1181
• Page End: 1202
• Publication Date: 2014-08-08
• Subjects: Null controllability, -- Carleman inequalities, -- Leray-αmodel, -- Navier−Stokes equations; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2014011
• Languages: English
• ISSNs: 1292-8119

Abstract

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 .