no. 2
Homogenization of the Stokes system in a thin film flow with rapidly varying thickness
ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 2, pp. 205-234 
@article{M2AN_1989__23_2_205_0,
     author = {Bayada, Guy and Chambat, Mich\`ele},
     title = {Homogenization of the {Stokes} system in a thin film flow with rapidly varying thickness},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {205--234},
     year = {1989},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {23},
     number = {2},
     mrnumber = {1001328},
     zbl = {0675.76033},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1989__23_2_205_0/}
}
TY  - JOUR
AU  - Bayada, Guy
AU  - Chambat, Michèle
TI  - Homogenization of the Stokes system in a thin film flow with rapidly varying thickness
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1989
SP  - 205
EP  - 234
VL  - 23
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - https://www.numdam.org/item/M2AN_1989__23_2_205_0/
LA  - en
ID  - M2AN_1989__23_2_205_0
ER  - 
%0 Journal Article
%A Bayada, Guy
%A Chambat, Michèle
%T Homogenization of the Stokes system in a thin film flow with rapidly varying thickness
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1989
%P 205-234
%V 23
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U https://www.numdam.org/item/M2AN_1989__23_2_205_0/
%G en
%F M2AN_1989__23_2_205_0
Bayada, Guy; Chambat, Michèle. Homogenization of the Stokes system in a thin film flow with rapidly varying thickness. ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 2, pp. 205-234. https://www.numdam.org/item/M2AN_1989__23_2_205_0/

[1] G. Bayada et M. Chambat, The transition between the Stokes equations and the Reynolds equation: a mathematical proof, Appl. Math. Opt. 14 (1986)73-93. | Zbl | MR

[2] G. Bayada et M. Chambat, On the various aspects of the thin film equation in hydrodynamic lubrification when the roughness occurs, in « Applications of multiple scaling in mechanics », Masson, Paris 1987. | Zbl | MR

[3] M. Chambart, G. Bayada et J. B. Faure, Some effects of the boundary roughness in a thin film flow, in « Boundary variation and boundary control », Proc. IFIP Conf. Nice, 1986, Lect. Notes Control Inf. Sciences, 100, Springer Verlag, Berlin 1988. | Zbl | MR

[4] G. Bayada et J. B. Faure, Application des techniques d'homogénéisation à des phénomènes de rugosité en lubrification hydrodynamique, Publications U.A. 740 CNRS Lyon St Etienne, 32 (1984) 1-52.

[5] A. Bensoussan, J. L. Lions et G. Papanicolaou, Asymptotic analysis for periodic structure, North Holland, Amsterdam 1978. | Zbl | MR

[6] D. Caillerie, Homogénéisation des équations de la diffusion stationnaire dans des domaines cylindriques aplatis, RAIRO Anal. Num.,15 (4) (1981) 295-319. | Zbl | MR | Numdam

[7] D. Caillerie, Thin Elastic and Periodic Plates, Math. Meth. in the Appl. Sci., 6 (1984) 159-191. | Zbl | MR

[8] K. K. Chen et D. C. Sun, On the statistical treatment of rough surface in hydrodynamic lubrication problems, Proc. of the 4th Leeds-Lyon Symp. on surface roughness in lubrication, IME (1977) 41-45.

[9] H. Christensen et K. Tonder, The hydrodynamic lubrication of rough bearing surfaces of finite width, J. of Lub. Tech., Trans. ASME, F, 93 (3) (1971) 324-330.

[10] V. Girault et P. A. Raviart, Finite element approximation of the Navier-Stokes equations, Springer Verlag, Berlin, 1981. | Zbl | MR

[11] R. Kohn et M. Vogelius, A new model for thin plates with rapidly varying thickness, Int. J. Solid and Struct., 20 (1984) 333-350. | Zbl

[12] R. Kohn et M. Vogelius, A new model for thin plates with rapidly varying thickness II. a convergence proof, Quart. of Appl Math. 18 (1985) 1-22. | Zbl | MR

[13] J. L. Lions, Perturbations singulières dans les problèmes aux limites en contrôle optimal, Springer Verlag, Berlin, 1973. | Zbl | MR

[14] N. Patir et H. S Cheng, An average flow model for determining effects of three dimensional roughness in partial hydrodynamic roughness, J of Lub. Tech., Trans. ASME, F 100 (1978) 12-17.

[15] N. Phan Thien, On the effects of the Reynolds and Stokes roughness in a two dimensional slider hearing, Proc. R. Soc. London, A377 (1981) 349-362. | Zbl

[16] N. Phan Thien, Hydrodynamic lubrication of rough surfaces, Proc. R. Soc. London, A383 (1982) 439-446. | Zbl

[17] J. Saint Jean Paulin, Homogénéisation et perturbations dans un problème lié à l'échauffement d'un câble électrique, Ann Fac. Sc., Toulouse 5 (1983) 43-59. | Zbl | MR | Numdam

[18] E. Sanchez-Palencia, Non homogeneous media and vibration theory, Lecture Notes in Physics 127, Springer Verlag, Berlin, 1978. | Zbl | MR

[19] D. C. Sun and K. K Chen, First effects of Stokes roughness on hydrodynamic lubrication, J. of Lub Tech., Trans. ASME, F, 99 (1977) 2-5.

[20] L. Tartar, Cours Peccot, Collège de France, 1977.

[21] J. L. Teale et A. O. Lebeck, An évaluation of the average flow model for surface roughness effects in lubrication, J. of Lub. Tech., Trans. ASME, F, 102 (1980) 360-367.

[22] R. Temam, Navier Stokes equation, North Holland, Amsterdam, 1979.