  We consider the incompressible, two dimensional Navier Stokes equation with
periodic boundary conditions under the effect of an additive, white in time,
stochastic forcing. Under mild restrictions on the geometry of the scales
forced, we show that any finite dimensional projection of the solution
possesses a smooth density with respect to Lebesgue measure. We also show that
under natural assumptions the density of such a projection is everywhere
strictly positive. In particular, our conditions are viscosity independent. We
are mainly interested in forcing which excites a very small number of modes.
All of the results rely on the nondegeneracy of the infinite dimensional
Malliavin matrix.
