Homogenization of incompressible generalized Stokes ows through a porous medium

Abstract

We study the homogenization for families of steady and also unsteady incompressible generalized Stokes systems in a periodic porous medium. We assume that the stress tensor possesses an Orlicz growth and the size of solid parts of the porous medium is comparable to the size of the period.

Homogenized systems are established using the two-scale convergence method adopted to Orlicz space setting. We prove the existence and uniqueness of weak solutions of the homogenized systems.

Keywords

• porous media flow
• non-Newtonian fluid
• shear-dependent viscosity, Orlicz space
• periodic homogenization
• two-scale convergence method