Stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients

TL;DR

This paper establishes stochastic homogenization for 2D Navier--Stokes equations with random coefficients, showing solutions converge in distribution to those with constant coefficients using weak convergence and averaging methods.

Contribution

It introduces a novel approach combining weak convergence and Stratonovich--Khasminskii averaging to analyze stochastic homogenization in fluid dynamics.

Findings

Solutions converge in distribution to deterministic equations

Method applies to equations with random coefficients

Provides a rigorous framework for stochastic homogenization

Abstract

This paper derives the stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients. By means of weak convergence method and Stratonovich--Khasminskii averaging principle approach, the solution of two dimensional Navier--Stokes equations with random coefficients converges in distribution to the solution of two dimensional Navier--Stokes equations with constant coefficients.