Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity
type: Item
instance of: scholarly article
title: Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity
zbMATH Open document ID: 0953.37023
author: Jonathan C. Mattingly
published in: Communications in Mathematical Physics
publication date: 2000-01-17T00:00:00Z
review text: It is shown that a two-dimensional, incompressible Navier-Stokes equation, forced additively by a Gauss random field, which is white in time, has a unique invariant measure, provided the viscosity is large enough. The proof proceeds by constructing a stationary solution, obtained by starting at a negative time, and then letting the initial time tend to \(-\infty\). The law of this stationary solution is the invariant measure. The method used in this paper is a special case of a method used for the construction of random attractors. The present result can be restated by saying that for large viscosity the attractor is a one-point set. Similar results have recently been obtained by \textit{B. Schmalfuß} [Stochastic Anal. Appl. 17, No. 6, 1075-1101 (1999; Zbl 0944.60071)].
Mathematics Subject Classification ID: 37L55
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1389278
zbMATH Keywords: incompressible Navier-Stokes equation
zbMATH Keywords: Gauss random field
zbMATH Keywords: invariant measure
zbMATH Keywords: random attractors
reviewed by: Hans Crauel
MaRDI profile type: Publication
full work available at URL: s002200050706
OpenAlex ID: W1991750711
DOI: 10.1007/S002200050706
description: scientific article; zbMATH DE number 1389278