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Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

J. Bricmont·A. Kupiainen·R. Lefevere
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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 $ν$, and grows like $ν^{-3}$ when $ν$ goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time.

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J. Bricmont, A. Kupiainen, R. Lefevere. 2000-10-20. Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics. https://arxiv.org/abs/math-ph/0010028

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