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

摘要

We consider the Stokes system in a thin porous medium $Omega_arepsilon$ ofthickness $arepsilon$ which is perforated by periodically distributed solidcylinders of size $arepsilon$. On the boundary of the cylinders we prescribenon-homogeneous Fourier boundary condition depending on a parameter $gamma$.The aim is to give the asymptotic behavior of the velocity and the pressure ofthe fluid as $arepsilon$ goes to zero. Using an adaptation of the unfoldingmethod, we give, following the values of $gamma$, different limit systems.