Homogenization of a non-stationary Stokes flow in porous medium including a layer

We study the behavior of the solution to the non-stationary Stokes equations in a porous medium with characteristic size of the pores ε and containing a thin fissure {0⩽xn⩽η} of width η. The limit when ε and η tend to zero gives the homogenized behavior of the flow, which depends on the comparison between ε and η.