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Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

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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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Authors and Affiliations

  1. UCL, Physique Théorique, 1348 Louvain-la-Neuve, Belgium, , , , , , BE

    J. Bricmont

  2. Helsinki University, Department of Mathematics, P.O. Box 4, Helsinki 00014, Finland;, , , , , , FI

    A. Kupiainen  & R. Lefevere

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  1. J. Bricmont
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  2. A. Kupiainen
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  3. R. Lefevere
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Received: 14 March 2002 / Accepted: 7 May 2002 Published online: 22 August 2002

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Bricmont, J., Kupiainen , A. & Lefevere, R. Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics. Commun. Math. Phys. 230, 87–132 (2002). https://doi.org/10.1007/s00220-002-0708-1

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  • DOI: https://doi.org/10.1007/s00220-002-0708-1

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