@article{1206.35266,
author="Birnir, Bj\"orn",
title="{Existence, uniqueness and statistical theory of turbulent solutions of
    the stochastic Navier-Stokes equation, in three dimensions -- an
    overview.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="1",
pages="53-86",
year="2010",
abstract="{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.}",
reviewer="{Elisa Al\`os (Barcelona)}",
keywords="{turbulence; uniqueness; invariant measures; blow-up; stochastic
    equation}",
classmath="{*35R60 (PDE with randomness)
35Q30 (Stokes and Navier-Stokes equations)
76F02 (Fundamentals)
76F55 (Statistical turbulence modeling)
60H15 (Stochastic partial differential equations)
}",
}