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Ergodicity for the Randomly Forced 2D Navier–Stokes Equations

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Abstract

We study space-periodic 2D Navier–Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N 0 coefficients (where N 0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, U.K.

    Sergei Kuksin & Armen Shirikyan

  2. Steklov Institute of Mathematics, 8 Gubkina St., 117966, Moscow, Russia

    Sergei Kuksin

  3. Institute of Mechanics of MSU, 1 Michurinskii Av., 119899, Moscow, Russia

    Armen Shirikyan

Authors
  1. Sergei Kuksin
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  2. Armen Shirikyan
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Kuksin, S., Shirikyan, A. Ergodicity for the Randomly Forced 2D Navier–Stokes Equations. Mathematical Physics, Analysis and Geometry 4, 147–195 (2001). https://doi.org/10.1023/A:1011989910997

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  • DOI: https://doi.org/10.1023/A:1011989910997

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