  We study controllability issues for the Navier-Stokes Equation on a two
dimensional rectangle with so-called Lions boundary conditions. Rewriting the
Equation using a basis of harmonic functions we arrive to an
infinite-dimensional system of ODEs. Methods of Geometric/Lie Algebraic Control
Theory are used to prove controllability by means of low modes forcing of
finite-dimensional Galerkin approximations of that system. Proving the
continuity of the ``control $\mapsto$ solution'' map in the so-called
relaxation metric we use it to prove both solid controllability on observed
component and $\mathbf L^2$-approximate controllability of the Equation (full
system) by low modes forcing.
