Stochastic Navier-Stokes equation and renormalization group theory
type: Item
instance of: scholarly article
title: Stochastic Navier-Stokes equation and renormalization group theory
zbMATH Open document ID: 1021.35078
DOI: 10.1016/S0167-2789(02)00621-8
author: D. Blömker
author: Christoph Gugg
author: Stanislaus Maier-Paape
published in: Physica D
publication date: 2002-11-13T00:00:00Z
review text: The authors deal with the stochastic Navier-Stokes equation for the velocity field \(u\) and the pressure \(p\) with periodic boundary conditions in a 2D domain \(\Omega=(0,2\pi a_1)\times (0,2\pi a_2)\): \[ \frac{\partial u}{\partial t}-\nu\Delta u+(u\cdot\nabla)u+\nabla p=f+\sqrt\varepsilon \eta,\quad \text{div} u=0\text{ in }\Omega, \quad \int_\Omega u dx=0,\quad u|_{t=0}=u_0, \] where \(\nu>0\), \(a_1,a_2>0\); \(a_1^{-2}\) and \(a_2^{-2}\) are rationally independent in order to avoid certain resonant terms. The forcing \(f+\sqrt\varepsilon \eta\) consists of a time-independent mean forcing \(f=f(x)\) and some small stochastic fluctuation \(\sqrt\varepsilon \eta\), \(\varepsilon\) is a small positive parameter. The authors present an application of a certain renormalization group theory (developed by Chen, Coldenfeld, and Oono). Since the classical renormalization group theory utilizes significantly on adding noise terms in order to similate high oscillating fluctuations, the authors' approach can be considered as another step towards a rigorous understanding of previous models.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1828079
zbMATH Keywords: additive gaussian noise
zbMATH Keywords: periodic boundary conditions
zbMATH Keywords: stochastic Navier-Stokes equation
zbMATH Keywords: renormalization group theory
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: The stochastic Landau equation as an amplitude equation
cites work: Renormalization Group Theory for Global Asymptotic Analysis
cites work: Q2946507
cites work: On the approximation of the stochastic Burgers equation
cites work: Renormalization group method. Application to Navier-Stokes equation
cites work: Renormalization group method. Applications to partial differential equations
cites work: Stochastic Equations in Infinite Dimensions
cites work: Ergodicity for Infinite Dimensional Systems
cites work: Renormalization group derivation of phase equations
cites work: Q4841248
cites work: On a certain renormalization group method.
full work available at URL: s0167-2789(02)00621-8
OpenAlex ID: W2017659603
description: scientific article; zbMATH DE number 1828079