UNIFORM LOCAL NULL CONTROL OF THE LERAY-alpha MODEL

作者：Araruna Fagner D^*; Fernandez Cara Enrique; Souza Diego A

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2014, 20(4): 1181-1202.

DOI：10.1051/cocv/2014011

• Null controllability
• Carleman inequalities
• Leray-alpha model
• Navier-Stokes equations

This paper deals with the distributed and boundary controllability of the so called Leray-alpha model. This is a regularized variant of the Navier-Stokes system (alpha is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-alpha equations are locally null controllable, with controls bounded independently of alpha. We also prove that, if the initial data are sufficiently small, the controls converge as alpha -> 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.

• 出版日期2014-10