Exponential mixing of the 2D stochastic Navier-Stokes dynamics
type: Item
instance of: scholarly article
title: Exponential mixing of the 2D stochastic Navier-Stokes dynamics
zbMATH Open document ID: 1033.76011
author: J. Bricmont
author: Antti Kupiainen
author: Raphaël Lefevere
published in: Communications in Mathematical Physics
publication date: 2002-12-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0010028
review text: The Navier-Stokes equation on two-dimensional torus with a random force is under consideration. It is supposed that the force is white noise in time and excites only a finite number of modes. The number of excited modes depends on the viscosity \(\nu\) and grows like \(\nu^{-3}\) as \(\nu\to 0\). The authors use a Lyapunov-Schmidt type reduction to transform the original infinite-dimensional Markov process to a certain non-Markovian finite-dimensional one, and employ standard ideas of statistical mechanics to deduce the mixing properties of the dynamics. It is proved that the Markov process (describing the solution) has a unique invariant measure and is exponentially mixing in time.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 76D06
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1839149
zbMATH Keywords: two-dimensional torus
zbMATH Keywords: random force
zbMATH Keywords: white noise in time
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: Markov process
zbMATH Keywords: statistical mechanics
zbMATH Keywords: invariant measure
MaRDI profile type: Publication
OpenAlex ID: W1712238359
arXiv ID: math-ph/0010028
DOI: 10.1007/S00220-002-0708-1
description: scientific article