Journal of Dynamical and Control Systems

, Volume 12, Issue 4, pp 517–562

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


DOI: 10.1007/s10883-006-0004-z

Cite this article as:
Rodrigues, S. J Dyn Control Syst (2006) 12: 517. doi:10.1007/s10883-006-0004-z


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.

Key words and phrases.

Incompressible fluid two-dimensional Navier-Stokes system controllability 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.SISSA-ISASTriesteItaly
  2. 2.University of AveiroPortugal