J.Bricmont, A.Kupiainen, R.Lefevere
Exponential Mixing of the 2D Stochastic Navier-Stokes
Dynamics
(460K, postscript)
ABSTRACT. We consider the Navier-Stokes equation on a
two dimensional torus with a random force which is white noise
in time, and excites only
a finite number of modes. The number of excited
modes depends on the viscosity $\nu$, and
grows like $\nu^{-3}$ when $\nu$
goes to zero. We prove that this Markov process
has a unique invariant measure and is
exponentially mixing in time.