Continuity of the Darcy's law in the low-volume fraction limit
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 4, p. 475-499
@article{ASNSP_1991_4_18_4_475_0,
     author = {Allaire, Gr\'egoire},
     title = {Continuity of the Darcy's law in the low-volume fraction limit},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 18},
     number = {4},
     year = {1991},
     pages = {475-499},
     zbl = {0755.35084},
     mrnumber = {1153702},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1991_4_18_4_475_0}
}
Allaire, Grégoire. Continuity of the Darcy's law in the low-volume fraction limit. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 4, pp. 475-499. http://www.numdam.org/item/ASNSP_1991_4_18_4_475_0/

[1] G. Allaire, Homogenization of the Stokes flow in a connected porous medium, Asymptotic Anal. 2, 3, (1989) pp. 203-222. | MR 1020348 | Zbl 0682.76077

[2] G. Allaire, Homogénéisation des équations de Stokes dans un domaine perforé de petits trous répartis périodiquement, C. R. Acad. Sci. Paris, Sér. I, 309, 11, (1989) pp. 741-746. | MR 1054290 | Zbl 0696.73010

[3] G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes, Arch. Rational Mech. Anal., 113, (1991) pp. 209-298. | MR 1079189 | Zbl 0724.76021

[4] G. Allaire, Homogenization of the Navier-Stokes equations with a slip boundary condition, Comm. Pure Appl. Math., XLIV, (1991) pp. 605-641. | MR 1109374 | Zbl 0738.35059

[5] A. Bensoussan - J.L. Lions - G. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland (1978). | MR 503330 | Zbl 0404.35001

[6] D. Cioranescu - F. Murat, Un terme étrange venu d'ailleurs, Nonlinear partial differential equations and their applications, Collège de France seminar, Vol. 2 & 3, ed. by H, Brézis & J.L. Lions, Research notes in mathematics 60 & 70, Pitman, London (1982). | Zbl 0496.35030

[7] E. De Giorgi, G-operateurs and r-convergence, Proceedings of the International Congress of Mathematicians (Warsazwa, August 1983), PWN Polish Scientific Publishers and North Holland, (1984) pp. 1175-1191. | Zbl 0568.35025

[8] R. Finn, D. Smith, On the linearized hydrodynamical equations in two dimensions, Arch. Rational Mech. Anal., 25, (1967) pp. 1-25. | MR 211668 | Zbl 0152.45001

[9] H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech., 5, (1959) pp. 317-328. | MR 102285 | Zbl 0086.19901

[10] J.B. Keller, Darcy's law for flow in porous media and the two-space method, Lecture Notes in Pure and Appl. Math., 54, Dekker, New York (1980). | MR 577105 | Zbl 0439.76017

[11] O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach (1969). | MR 254401 | Zbl 0184.52603

[12] T. Levy, Fluid flow through an array of fixed particles, Internat. J. Engrg. Sci., 21, (1983) pp. 11-23. | MR 691100 | Zbl 0539.76092

[13] T. Levy - E. Sanchez-Palencia, Einstein-like approximation for homogenization with small concentration. II - Navier-Stokes equations, Nonlinear Anal., 9, 11, (1985) pp. 1255-1268. | MR 813657 | Zbl 0581.76097

[14] J.L. Lions, Some methods in the mathematical analysis of systems and their control, Beijing, Gordon and Breach, New York (1981). | MR 664760 | Zbl 0542.93034

[15] R. Lipton - M. Avellaneda, Darcy's law for slow viscous flow past a stationary array of bubbles, Proc. Roy. Soc. Edinburgh, 114A, (1990) pp. 71-79. | MR 1051608 | Zbl 0850.76778

[16] F. Murat, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, mimeographed notes (1978).

[17] R.S. Rayleigh, On the influence of obstacles arranged in rectangular order upon the properties of medium, Phil. Mag. 34, (1892) pp. 481-502. | JFM 24.1015.02

[18] E. Sanchez-Palencia, On the asymptotics of the fluid flow past an array of fixed obstacles, Internat. J. Engrg. Sci., 20, (1982) pp. 1291-1301. | MR 678289 | Zbl 0501.76086

[19] E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Phys. 127, Springer Verlag (1980). | MR 578345 | Zbl 0432.70002

[20] E. Sanchez-Palencia, Einstein-like approximation for homogenization with small concentration. I - Elliptic problems, Nonlinear Anal. 9, 11, (1985) pp. 1243-1254. | MR 813656 | Zbl 0538.76086

[21] A.S. Sangani, A. Acrivos, Slow flow through a periodic array of spheres, Internal. J. Multiphase Flow, 8, 4, (1982) pp. 343-360. | Zbl 0541.76041

[22] L. Tartar, Convergence of the homogenization process, Appendix of [19].

[23] L. Tartar, Cours Peccot au Collège de France, Unpublished (mars 1977).