Darcy's law for evolving microstructure

A Darcy law for evolving microstructure is derived by homogenisation of Stokes flow. We transform the equations from locally domain onto a periodic reference domain. There, we pass to limit employing method two-scale convergence. After transforming back its original domain, obtain Law microstructure. This does not only capture space- and time-dependent permeability, but also includes how change porosity induces pressure. In order give uniform priori estimates, derive Korn-type inequality this transformation as well family ϵ-scaled operators div−1ϵ.