Geodesic
Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 72-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

One considers flow past a body in an electrically conductive viscous fluid in magnetic field, the fluid being subject to a nonlinear rheological law. Solutions of the corresponding system of magnetohydrodynamic boundary layer are examined in a neighborhood of a frontal critical point. 
@article{TSP_2019_32_32_a3,
     author = {R. R. Bulatova and V. N. Samokhin and G. A. Chechkin},
     title = {Equations of symmetric {MHD-boundary} layer of viscous fluid with {Ladyzhenskaya} rheology law},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {72--90},
     year = {2019},
     volume = {32},
     number = {32},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a3/}
}
TY  - JOUR
AU  - R. R. Bulatova
AU  - V. N. Samokhin
AU  - G. A. Chechkin
TI  - Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law
JO  - Trudy Seminara im. I.G. Petrovskogo
PY  - 2019
SP  - 72
EP  - 90
VL  - 32
IS  - 32
UR  - http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a3/
LA  - ru
ID  - TSP_2019_32_32_a3
ER  - 
%0 Journal Article
%A R. R. Bulatova
%A V. N. Samokhin
%A G. A. Chechkin
%T Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law
%J Trudy Seminara im. I.G. Petrovskogo
%D 2019
%P 72-90
%V 32
%N 32
%U http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a3/
%G ru
%F TSP_2019_32_32_a3
R. R. Bulatova; V. N. Samokhin; G. A. Chechkin. Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 72-90. http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a3/

[1] Prandtl L., “Über Flüssigkeitsbewegungen bei sehr kleiner Reibund”, Verh. Int. Math. Kongr. (Heidelberg, 1904), Teubner, 1905, 484–494

[2] Leray J., “Étude des diverses équation intégrales nonlinéares et de quelques problèmes que pose l'Hydrodynamique”, J. Math. Pure Appl., 12 (1933), 1–82 | MR

[3] Schlichting H., Gersten K., Boundary-Layer Theory, Springer, Berlin, 2000 | MR | Zbl

[4] Temam R., Wang X., “Remarks on the Prandtl equation for a permeable wall”, Z. Angew. Math. Mech., 80:11-12 (2000), 835–843 | 3.0.CO;2-9 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[5] E. Weinan, “Boundary layer theory and the zero-viscosity limit of the Navier–Stokes equation”, Acta Math. Sin. (Engl. Ser.), 16:2 (2000), 207–218 | DOI | MR | Zbl

[6] Lopes Filho M. C., “Boundary layers and the vanishing viscosity limit for incompressible 2D flow”, Lectures on the analysis of nonlinear partial differential equations, v. 1, Morningside Lect. Math., 1, Int. Press, Somerville, 2012, 1–29 | MR

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

[8] 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 | Zbl

[9] Spiridonov S. V., “O teoreme usredneniya dlya stratifitsirovannoi magnitnoi zhidkosti s mikroneodnorodnymi magnitnym polem i granichnym usloviem”, Probl. matem. anal., 44 (2010), 133–143

[10] Spiridonov S. V., Chechkin G. A., “Prosachivanie pogranichnogo sloya nyutonovskoi zhidkosti cherez perforirovannuyu pregradu”, Probl. matem. anal., 45 (2010), 93–102 | Zbl

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

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

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

[14] Linkevich A. Yu., Ratyu T. S., Spiridonov S. V., Chechkin G. A., “O tonkom sloe nenyutonovskoi zhidkosti na sherokhovatoi poverkhnosti, protekayuschei cherez perforirovannuyu pregradu”, Probl. matem. anal., 68 (2013), 173–182 | MR

[15] Linkevich A. Yu., Samokhin V. N., Spiridonov S. V., Chechkin G. A., “Usrednenie modifitsirovannoi zhidkosti O. A. Ladyzhenskoi, protekayuschei cherez poristuyu pregradu”, Izv. vyssh. ucheb. zaved. Problemy poligrafii i izdatelskogo dela, 2016, no. 2, 2–35

[16] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka; Fizmatlit, M., 1970

[17] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Uravneniya pogranichnogo sloya dlya modifitsirovannoi sistemy Nave–Stoksa”, Tr. semin. im. I. G. Petrovskogo, 28, 2010, 329–361

[18] Vvedenskaya N. D., “O reshenii uravnenii pogranichnogo sloya v okrestnosti kriticheskoi tochki”, Zh. vychisl. mat. i matem. fiz., 7 (1967), 924–929

[19] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970

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

[21] Samokhin V. N., Chechkin G. A., “Uravneniya pogranichnogo sloya obobschenno nyutonovskoi sredy v okrestnosti kriticheskoi tochki”, Tr. semin. im. I. G. Petrovskogo, 31, 2016, 158–176

[22] Bulatova R. R., Samokhin V. N., Chechkin G. A., “Uravneniya MGD-pogranichnogo sloya dlya vyazkoi neszhimaemoi sredy v modifikatsii O. A. Ladyzhenskoi. Suschestvovanie i edinstvennost reshenii, vliyanie magnitnogo polya na yavlenie otryva pogranichnogo sloya”, Probl. matem. anal., 2018, no. 91 | Zbl