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Zbl 1206.35266
Birnir, Björn
Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview. (English)
[J] Banach J. Math. Anal. 4, No. 1, 53-86, electronic only (2010). ISSN 1735-8787/e

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 Alòs (Barcelona)]

MSC 2000:: *35R60 PDE with randomness
35Q30 Stokes and Navier-Stokes equations
76F02 Fundamentals
76F55 Statistical turbulence modeling
60H15 Stochastic partial differential equations

Keywords: turbulence; uniqueness; invariant measures; blow-up; stochastic equation

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