Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions
María Anguiano, ,Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160, 41080-Sevilla, Spain, Francisco J. Suárez‐Grau, ,Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012-Sevilla, Spain · Networks and Heterogeneous Media · 2019
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.