Mikelić, A. Homogenization of nonstationary Navier-Stokes equations in a domain with a grained boundary. (English) Zbl 0758.35007 Ann. Mat. Pura Appl., IV. Ser. 158, 167-179 (1991). Summary: We prove the convergence of the homogenization process for a nonstationary Navier-Stokes system in a porous medium. The result of homogenization is Darcy’s law, as in the case of the Stokes equation, but the convergence of pressures is in a different function space. Cited in 40 Documents MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 76D05 Navier-Stokes equations for incompressible viscous fluids 76S05 Flows in porous media; filtration; seepage Keywords:a priori estimates for pressure; convergence of the homogenization process; Darcy’s law PDF BibTeX XML Cite \textit{A. Mikelić}, Ann. Mat. Pura Appl. (4) 158, 167--179 (1991; Zbl 0758.35007) Full Text: DOI OpenURL References: [1] Bensoussan, A.; Lions, J. L.; Papanicolau, G., Asympotic analysis for periodic structures (1978), Amsterdam: North-Holland, Amsterdam [2] Cattabriga, L., Su un problema di contorno relativo ai sistemi di equazioni di Stokes, Rend. Mat. Sem. Univ. Padova, 31, 308-340 (1961) · Zbl 0116.18002 [3] Grisvard, P., Elliptic problems in non-smooth domains (1985), London: Pitman, London · Zbl 0695.35060 [4] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Paris: Dunod, Paris · Zbl 0189.40603 [5] Rudin, W., Functional analysis (1973), New York: McGraw-Hill, New York · Zbl 0253.46001 [6] Sanchez-Palencia, E., Nonhomogeneous media and vibration theory, Lecture Notes in Physics,127 (1980), Berlin: Springer-Verlag, Berlin [7] Tartar, L., Incompressible fluid flow in a porous medium-convergence of the homogenization process, Appendix to Lecture Notes in Physics,127 (1980), Berlin: Springer-Verlag, Berlin [8] Temam, R., Navier-Stokes equations (1979), Amsterdam: North-Holland, Amsterdam This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.