2024-05-032024-05-032018-02-050956-7925https://hdl.handle.net/11441/157559We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ε and containing a thin fissure of width ηε. The viscosity is supposed to obey the power law with flow index 5/3 ≤ q ≤ 2. The limit when size of the pores tends to zero gives the homogenized behavior of the flow. We obtain three different models depending on the magnitude ηε with respect to ε: if ηε ≪ ε^{q/(2q−1)} the homogenized fluid flow is governed by a time-dependent nonlinear Darcy law, while if ηε ≫ ε^{q/(2q−1)} is governed by a time-dependent nonlinear Reynolds problem. In the critical case, ηε ≈ ε^{q/(2q−1)} , the flow is described by a time-dependent nonlinear Darcy law coupled with a time-dependent nonlinear Reynolds problem.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Non-Newtonian flow; Non-stationary Stokes equation; Darcy’s law; porous medium; fissure.info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1017/S0956792518000049