Homogenization of a stationary flow of a generalized Newtonian fluid

TL;DR

This paper develops a homogenization method for stationary flows of generalized Newtonian fluids that bypasses the need for weak formulation testing, focusing on the stress tensor's dependence on solution sequences.

Contribution

It introduces a novel homogenization approach that avoids testing weak formulations, emphasizing the stress tensor's relation to solution sequences in generalized Newtonian fluid flows.

Findings

Stress tensor depends on the limit of solution sequences.

Homogenization process does not require testing weak formulations.

Method applicable to stationary generalized Newtonian fluid flows.

Abstract

We perform the homogenization process avoiding the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions. We show that the stress tensor for homogenized problem depends on the gradient involving the limit of a sequence selected from a family of solutions of initial problems.