Geodesic
Homogenization of stratified dilatant fluid
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 75-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study the behavior of the stationary magnetic hydrodynamical boundary layer of a dilatant fluid flowing through a porous obstacle. We consider a family of boundary value problems with a small parameter where micro-inhomogeneities are concentrated on the boundary of the domain (the original velocity profile depends on a small parameter). We construct an averaged problem and prove convergence of the solution of the original problem to that of the averaged one. Thus we describe the effective behavior of the micro-inhomogeneous fluid. 
@article{CMFD_2013_48_a5,
     author = {A. Yu. Linkevich and S. V. Spiridonov and G. A. Chechkin},
     title = {Homogenization of stratified dilatant fluid},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {75--83},
     publisher = {mathdoc},
     volume = {48},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_48_a5/}
}
TY  - JOUR
AU  - A. Yu. Linkevich
AU  - S. V. Spiridonov
AU  - G. A. Chechkin
TI  - Homogenization of stratified dilatant fluid
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2013
SP  - 75
EP  - 83
VL  - 48
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2013_48_a5/
LA  - ru
ID  - CMFD_2013_48_a5
ER  - 
%0 Journal Article
%A A. Yu. Linkevich
%A S. V. Spiridonov
%A G. A. Chechkin
%T Homogenization of stratified dilatant fluid
%J Contemporary Mathematics. Fundamental Directions
%D 2013
%P 75-83
%V 48
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2013_48_a5/
%G ru
%F CMFD_2013_48_a5
A. Yu. Linkevich; S. V. Spiridonov; G. A. Chechkin. Homogenization of stratified dilatant fluid. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 75-83. http://geodesic.mathdoc.fr/item/CMFD_2013_48_a5/

[1] Linkevich A. Yu., Spiridonov S. V., Chechkin G. A., “O pogranichnom sloe nyutonovskoi zhidkosti, obtekayuschei sherokhovatuyu poverkhnost i prokhodyaschei cherez perforirovannuyu pregradu”, Ufimskii mat. zhurn., 3:3 (2011), 93–104

[2] Linkevich A. Yu., Spiridonov S. V., Chechkin G. A., “Ob asimptoticheskom povedenii reshenii sistemy uravnenii Prandtlya dlya stratifitsirovannoi magnitnoi zhidkosti”, Mezhd. konf., posvyaschënnaya 110 godovschine vydayuschegosya matematika I. G. Petrovskomu, Tezisy dokladov, Izd-vo MGU i OOO “INTUIT.RU”, M., 2011, 256–257

[3] Oleinik O. A., Samokhin V. N., Matematicheskie metody v teorii pogranichnogo sloya, Nauka, Fizmatlit, M., 1997 | MR

[4] Romanov M. S., “Ob usrednenii pogranichnogo sloya psevdoplasticheskoi zhidkosti v prisutstvii bystroostsilliruyuschikh vneshnikh sil”, Tr. sem. im. I. G. Petrovskogo, 28, 2011, 300–328

[5] Romanov M. S., Samokhin V. N., Chechkin G. A., “O skorosti skhodimosti reshenii uravnenii Prandtlya v bystro ostsilliruyuschem magnitnom pole”, Dokl. RAN, 426:4 (2009), 450–456 | MR | Zbl

[6] Ryzhov O. S., Savenkov I. V., “Prostranstvennye vozmuscheniya, vnosimye garmonicheskim ostsillyatorom v pogranichnyi sloi na plastinke”, Zhurn. vych. mat. i mat. fiz., 28:4 (1988), 591–602 | MR | Zbl

[7] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Modifikatsiya O. A. Ladyzhenskoi uravnenii Nave–Stoksa i teoriya pogranichnogo sloya”, Vestnik MGUP im. Ivana Fedorova, 2009, no. 5, 127–143

[8] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “O nepreryvnoi zavisimosti resheniya uravnenii pogranichnogo sloya ot profilya nachalnykh skorostei”, Vestnik MGUP im. Ivana Fedorova, 2010, no. 4, 64–71

[9] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Asimptotika reshenii uravnenii pogranichnogo sloya obobschënno nyutonovskoi sredy pri vneshnem techenii, blizkom k simmetrichnomu”, Probl. mat. analiza, 59, 2011, 123–128 | MR

[10] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Attraktory sistemy uravnenii pogranichnogo sloya obobschënno nyutonovskoi sredy”, Vestnik MGUP im. Ivana Fedorova, 2011, no. 1, 245–249

[11] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Uravneniya pogranichnogo sloya dlya modifitsirovannoi sistemy Nave–Stoksa”, Tr. sem. im. I. G. Petrovskogo, 28, 2011, 329–361

[12] Spiridonov S. V., “Usrednenie reshenii statsionarnoi sistemy uravnenii pogranichnogo sloya dlya magnitnoi zhidkosti”, Mezhd. konf., posvyaschënnaya I. G. Petrovskomu, Tezisy dokladov, Izd-vo MGU, M., 2007

[13] Spiridonov S. V., “O teoreme usredneniya dlya stratifitsirovannoi magnitnoi zhidkosti s mikroneodnorodnymi magnitnym polem i granichnym usloviem”, Probl. mat. analiza, 44, 2010, 133–143 | MR

[14] Spiridonov S. V., Chechkin G. A., “Asimptoticheskoe povedenie reshenii statsionarnoi sistemy uravnenii pogranichnogo sloya dlya magnitnoi zhidkosti”, III mezhd. konf. “Matematicheskie idei P. L. Chebyshëva i ikh prilozhenie k sovremennym problemam estestvoznaniya” (14–18 maya, 2006, Obninsk, Rossiya), Izd-vo Obn. gos. tekh. un-ta atom. energ., Obninsk, 2006, 121–122

[15] Spiridonov S. V., Chechkin G. A., “Prosachivanie pogranichnogo sloya nyutonovskoi zhidkosti cherez perforirovannuyu pregradu”, Probl. mat. analiza, 45, 2010, 93–102 | MR

[16] Amirat Y., Chechkin G. A., Romanov M. S., “On multiscale homogenization problems in boundary layer theory”, Z. Angew. Math. Phys., 63:3 (2012), 475–502 | DOI | MR | Zbl

[17] Bayada G., Chambat M., “Homogenezation of the Stokes system in a thin film with rapidly varying thickness”, Model. Math. Anal. Number. ($\mathrm{M^2AN}$), 23:2 (1989), 205–234 | MR | Zbl

[18] Conca C., “On the application of the homogenization theory to a class of problems arising in fluid mechanics”, J. Math. Pures Appl. (9), 64:1 (1985), 31–75 | MR | Zbl