Homogenization and corrector results for the stochastic non-homogeneous incompressible Navier-Stokes equations
Zhaoyang Qiu, Junlong Chen, Jinqiao Duan
公開日: 2025/1/6
Abstract
In this paper we are concerned with the homogenization property of stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation in a smooth bounded domain of $\mathbb{R}^d$, $d=2,3$, and driven by multiplicative cylindrical Wiener noise. Using two-scale convergence, stochastic compactness and the martingale representative theory, we show the solutions of original equations converge to a solution of stochastic non-homogeneous incompressible version with constant coefficients. Additionally, a corrector result is provided, which strengthens the two-scale convergence from weak to strong within an appropriate regularity framework. Several challenges arising from stochastic effect and the limited regularity induced by the density function are addressed throughout the analysis.