an:05702399 Zbl 1206.35266 Birnir, Bj\"orn Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview. EN Banach J. Math. Anal. 4, No. 1, 53-86, electronic only (2010). ISSN 1735-8787/e 2010

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*35R60 35Q30 76F02 76F55 60H15 turbulence; uniqueness; invariant measures; blow-up; stochastic equation This paper is devoted to proofs of the existence and uniqueness of solutions of the Navier-Stokes equation driven with additive noise in three dimensions, in the presence of a strong uni-directional mean flow with some rotation. The authors discusses how the existence of a unique invariant measure is established and the properties of this measure are described. The invariant measure is used to prove Kolmogorov's scaling in 3-dimensional turbulence including the celebrated $-5/3$ power law for the decay of the power spectrum of a turbulent 3-dimensional flow. Then the author briefly describes the mathematical proof of Kolmogorov's statistical theory of turbulence. Elisa Al\`os (Barcelona)