Homogenization of incompressible generalized Stokes flows through a porous medium. (May 2016)

• Record Type: Journal Article
• Authors: Kalousek, Martin
• Is Part Of: Nonlinear analysis. Volume 136(2016)
• Page Start: 1
• Page End: 39
• Publication Date: 2016-05
• Subjects: Porous media flow -- Non-Newtonian fluid -- Shear-dependent viscosity -- Orlicz space -- Periodic homogenization -- Two-scale convergence method; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.01.025
• Languages: English
• ISSNs: 0362-546X

Abstract

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.