Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise

We prove ergodicity of the finite dimensional approximations of the three dimensional Navier–Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential. (preprint available at http://arxiv.org/pdf/math.PR/0210082.pdf)