, Volume 12, Issue 4, pp 517-562
Date: 22 Sep 2006

Navier-Stokes Equation on the Rectangle: Controllability by Means of Low Mode Forcing

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract.

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 L 2-approximate controllability of the Navier-Stokes equation (full system) by low mode forcing.

2000 Mathematics Subject Classification. 35Q30, 93C20, 93B05, 93B29.
Supported by FCT (Portuguese Foundation for Science and Technology).