Darcy's laws for non‐stationary viscous fluid flow in a thin porous medium
María Anguiano · Mathematical Methods in the Applied Sciences · 2016
We consider a non‐stationary Stokes system in a thin porous medium Ωϵ of thickness ϵ which is perforated by periodically solid cylinders of size aϵ. We are interested here to give the limit behavior when ϵ goes to zero. To do so, we apply an adaptation of the unfolding method. Time‐dependent Darcy's laws are rigorously derived from this model depending on the comparison between aϵ and ϵ. Copyright © 2016 John Wiley & Sons, Ltd.