On the effective equations of a viscous incompressible fluid flow through a filter of finite thickness

Communications on Pure and Applied Mathematics

Volumn 51, Issue 9-10, 1998, Pages 1073-1121

  Jäger, Willi ^a   Mikelić, Andro ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040039889     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0312(199809/10)51:9/10<1073::aid-cpa6>3.3.co;2-g     Document Type: Article

References (20)

1. Allaire, G., Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes II: Noncritical sizes of the holes for a volume distribution and a surface distribution of holes, Arch. Rational Mech. Anal., 113, 1990, pp. 261-298.
2. Allaire, G., and Mikelić, A., One-phase Newtonian flow, pp. 45-76, 259-275 in: Homogenization and Porous Media, U. Hornung, ed., Interdisciplinary Applied Mathematics No. 6, Springer-Verlag, New York, 1997.
3. Antontsev, S. N., Kazhikhov, A. V., and Monakhov, V. N., Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Studies in Mathematics and Its Applications No. 22, North-Holland, Amsterdam, 1990.
4. Brillard, A., Asymptotic flow of a viscous and incompressible fluid through a plane sieve, pp. 158-172 in: Progress in Partial Differential Equations, Calculus of Variations, Applications, C. Bandle, J. Bemelmans, M. Chipot, M. Grüter, and J. Saint Jean Paulin, eds., Pitman Research Notes in Mathematics Series No. 267, Longman, Harlow, England, 1992.
5. Conca, C., On the applications of the homogenization theory to a class of problems arising in fluid mechanics, J. Math. Pures Appl. (9) 64, 1985, pp. 31-75.
6. Conca, C., Étude d'un fluide traversant une paroi perforée I. Comportement limite près de la paroi, and II. Comportement limite loin de la paroi, J. Math. Pures Appl. 66, 1987, pp. 1-43, 45-70.
7. Conca, C., Murat, F., and Pironneau, O., The Stokes and Navier-Stokes equations with boundary conditions involving the pressure, Japan J. Math. (N. S.) 20, 1994, pp. 279-318.
8. Constantin, P., and Foias, C., Navier-Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, 1988.
9. Galdi, G. P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations II: Nonlinear Steady Problems, Springer Tracts in Natural Philosophy No. 39, Springer-Verlag, New York, 1994.
10. Iosif'yan, G. A., Saint-Venant's principle for flows of a viscous incompressible fluid and its applications, Trudy Moskov. Mat. Obshch. 43, 1981, pp. 3-36; Trans. Moscow Math. Soc., 43, 1983, pp. 1-37.
11. Iosif'yan, G. A., Saint-Venant's principle for flows of a viscous incompressible fluid and its applications, Trudy Moskov. Mat. Obshch. 43, 1981, pp. 3-36; Trans. Moscow Math. Soc., 43, 1983, pp. 1-37.
12. Jäger, W., and Mikelić, A., Homogenization of the Laplace equation in a partially perforated domain, preprint no. 157, Equipe d'Analyse Numérique Lyon-St-Etienne, September 1993.
13. Jäger, W., and Mikelić, A., On the boundary conditions at the contact interface between a porous medium and a free fluid, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23, 1996, pp. 403-465.
14. Jäger, W., Oleǐnik, O. A., and Shamaev, A. S., On the homogenization problem for the Laplace operator in a partially perforated domain with the Neumann condition on holes, Russian Acad. Sci. Dokl. Math. 48, 1994, pp. 545-551.
15. Lipton, R., and Avellaneda, M., Darcy's law for slow viscous flow past a stationary array of bubbles, Proc. Royal Soc. Edinburgh Sect. A 114, 1990. pp. 71-79.
16. Middleman, S., Modeling Axisymmetric Flows, Academic Press, San Diego, 1995.
17. Oleǐnik, O. A., and Iosif'yan, G. A., The behavioral infinity of the solutions of second-order elliptic equations in domains with a noncompact boundary, Math. USSR-Sb. 40, 1981, pp. 527-548.
18. Oleǐnik, O. A., Shamaev, A. S., and Yosifian, G. A., Mathematical Problems in Elasticity and Homogenization, Studies in Mathematics and Its Applications No. 26, North-Holland, Amsterdam, 1992.
19. Tartar, L., Incompressible fluid flow in a porous medium-convergence of the homogenization process, pp. 368-377 in: Non Homogeneous Media and Vibration Theory, Lecture Notes in Physics No. 127, Springer-Verlag, Berlin, 1980.
20. Temam, R., Navier-Stokes Equations: Theory and Numerical Analysis, 3rd ed., Studies in Mathematics and Its Applications No. 2, North-Holland, Amsterdam-New York, 1984.