On the non-stationary Navier-Stokes flows and reiterated homogenization

TL;DR

This paper investigates the homogenization of non-stationary Navier-Stokes equations with rapidly varying coefficients, establishing convergence, corrector results, and deriving the macroscopic model.

Contribution

It provides a new convergence theorem, a corrector result, and derives the homogenized model for non-stationary Navier-Stokes flows with periodic coefficients.

Findings

Proved a convergence theorem for reiterated homogenization.

Established a corrector result for the model.

Derived the macroscopic homogenized Navier-Stokes equations.

Abstract

We study the deterministic reiterated homogenization of the non-stationary Navier-Stokes type equations in fixed domains with periodically rapidly varying coefficients. One convergence theorem and a corrector result are proved, and we derive the macroscopic homogenized model.