Abstract
We consider the Navier–Stokes equation on a two-dimensional torus with a random force, white noise in time, and analytic in space, for arbitrary Reynolds number R. We prove probabilistic estimates for the long-time behavior of the solutions that imply bounds for the dissipation scale and energy spectrum as R→∞.
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Bricmont, J., Kupiainen, A. & Lefevere, R. Probabilistic Estimates for the Two-Dimensional Stochastic Navier–Stokes Equations. Journal of Statistical Physics 100, 743–756 (2000). https://doi.org/10.1023/A:1018627609718
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DOI: https://doi.org/10.1023/A:1018627609718