Navier-Stokes Equation on the Rectangle: Controllability by Means of Low Mode Forcing
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- Rodrigues, S. J Dyn Control Syst (2006) 12: 517. doi:10.1007/s10883-006-0004-z
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We study controllability issues for the Navier-Stokes equation on a two-dimensional rectangle under so-called Lions boundary conditions. The Navier-Stokes equation is controlled by forcing applied to a small number of harmonic modes. Methods of Geometric/Lie Algebraic Control Theory are used to prove controllability by means of low mode forcing of finite-dimensional Galerkin approximations of this system. Proving the continuity of the “control ↦ solution” mapping in the so-called relaxation metric we use it to prove both solid controllability on the observed component and L2-approximate controllability of the Navier-Stokes equation (full system) by low mode forcing.