Abstract
We prove ergodicity of the finite dimensional approximations of the three dimensional Navier–Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential.
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Romito, M. Ergodicity of the Finite Dimensional Approximation of the 3D Navier–Stokes Equations Forced by a Degenerate Noise. Journal of Statistical Physics 114, 155–177 (2004). https://doi.org/10.1023/B:JOSS.0000003108.92097.5c
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DOI: https://doi.org/10.1023/B:JOSS.0000003108.92097.5c