Stochastic Navier–Stokes equation and renormalization group theory

Abstract

We present an application of a certain renormalization group (RNG) theory developed by Chen, Goldenfeld, and Oono to the stochastic two-dimensional Navier–Stokes equation with additive Gaussian noise and periodic boundary conditions. This article is a generalization of results of Moise and Temam which were for the deterministic equation. Because the classical RNG theory (e.g. in a famous work by Yakhot and Orszag) utilizes significantly on adding noise terms, our work could be another step towards a rigorous understanding of their method.