Homogenization of an incompressible non-Newtonian flow through a thin porous medium

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In this paper, we consider a non-Newtonian flow in a thin porous medium \(\Omega _{\varepsilon }\) of thickness \(\varepsilon \) which is perforated by periodically solid cylinders of size \(a_{\varepsilon }\). The flow is described by the 3D incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index \(1<p<+\infty \). We consider the limit when domain thickness tends to zero, and we obtain different models depending on the magnitude \(a_{\varepsilon }\) with respect to \(\varepsilon \).