# American Institute of Mathematical Sciences

June  2019, 14(2): 289-316. doi: 10.3934/nhm.2019012

## Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions

 1 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160, 41080-Sevilla, Spain 2 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012-Sevilla, Spain

* Corresponding author: Francisco Javier Suárez-Grau

Received  April 2018 Revised  September 2018 Published  April 2019

Fund Project: María Anguiano is supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466. Francisco Javier Suárez-Grau is supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P

We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter $\gamma$. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid as $\varepsilon$ goes to zero. Using an adaptation of the unfolding method, we give, following the values of $\gamma$, different limit systems.

Citation: María Anguiano, Francisco Javier Suárez-Grau. Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions. Networks & Heterogeneous Media, 2019, 14 (2) : 289-316. doi: 10.3934/nhm.2019012
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##### References:
Views of a periodic cell in 2D (left) and 3D (right)
View of $\omega_\varepsilon$
Views of the domain $\Omega_\varepsilon$ (left) and $\Lambda_\varepsilon$ (right)
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