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

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Abstract

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 \(\varepsilon \).

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Correspondence to Francisco Javier Suárez-Grau.

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María Anguiano has been supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466, and in part by European Commission, Excellent Science—European Research Council (ERC) H2020-EU.1.1.-639227. F.J. Suárez-Grau has been supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P.

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Anguiano, M., Suárez-Grau, F.J. Homogenization of an incompressible non-Newtonian flow through a thin porous medium. Z. Angew. Math. Phys. 68, 45 (2017). https://doi.org/10.1007/s00033-017-0790-z

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