Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

Details Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

2000-10-20

arxiv.org/abs/math-ph/0010028v1

Physics

Mathematical Physics

Scientific paper

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.

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