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Open Access Publications from the University of California

Approximation of the Invariant Measure for the Stochastic Navier-Stokes

Abstract

Kolmogorov's statistical theory of turbulence is based on the existence of the invariant measure of the Navier-Stokes flow. Recently the existence of the invariant measure was established in the three-dimensional case. It was established earlier by the author for uni-directional flow and for rivers. We discuss how one can try to go about approximating the invariant measure in three dimensions.