Two-Scale Convergence of Unsteady Stokes Type Equations

TL;DR

This paper investigates the homogenization of unsteady Stokes equations with oscillating coefficients using two-scale convergence, extending classical models to more complex periodic settings.

Contribution

It introduces a homogenization framework for unsteady Stokes equations with divergence form operators and periodic coefficients, utilizing two-scale convergence.

Findings

Established homogenized equations for unsteady Stokes with oscillating coefficients

Extended two-scale convergence method to unsteady fluid flow models

Provided rigorous mathematical analysis for periodic homogenization

Abstract

In this paper we study the homogenization of unsteady Stokes type equations in the periodic setting. The usual Laplace operator involved in the classical Stokes equations is here replaced by a linear elliptic differential operator of divergence form with periodically oscillating coefficients. Our mean tool is the well known two-scale convergence method.