Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure

摘要: We consider a non-stationary incompressible non-Newtonian Stokes system in porous medium with characteristic size of the pores ϵ and containing thin fissure width η . The viscosity is supposed to obey power law flow index $\frac{5}{3}\leq q\leq 2$ limit when tends zero gives homogenized behaviour flow. obtain three different models depending on magnitude respect ϵ: if ≪ $\varepsilon^{q\over 2q-1}$ fluid governed by time-dependent non-linear Darcy law, while ≫ Reynolds problem. In critical case, ≈ , described coupled