Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview
type: Item
instance of: scholarly article
title: Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview
zbMATH Open document ID: 1206.35266
author: Björn Birnir
published in: Banach Journal of Mathematical Analysis
publication date: 2010-04-27T00:00:00Z
full work available at URL: https://eudml.org/doc/230012
full work available at URL: tex v4 n1 a5.pdf
review text: 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.
reviewed by: Elisa Alòs
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76F02
Mathematics Subject Classification ID: 76F55
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 5702399
zbMATH Keywords: turbulence
zbMATH Keywords: uniqueness
zbMATH Keywords: invariant measures
zbMATH Keywords: blow-up
zbMATH Keywords: stochastic equation
MaRDI profile type: Publication
OpenAlex ID: W2154017585
DOI: 10.15352/BJMA/1272374671
description: scientific article; zbMATH DE number 5702399