Uniform local null control of the Leray-α model∗∗∗. (8th August 2014) - Araruna, Fágner D.; Fernández-Cara, Enrique; Souza, Diego A.
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 .