Geodesic
O.~A.~Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 19-37.

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

In this paper, we study the system of equations of a boundary layer for a nonlinearly viscous, electrically conductive fluid described by a rheological law proposed by O. A. Ladyzhenskaya for incompressible media. The boundary-layer equations for the Ladyzhenskaya model were first obtained from Prandtl's axioms. By the Mises transform, the system of boundary-layer equations can be reduced to a single quasilinear equation. The main method used in this paper is the Crocco transform, which turns the system of boundary-layer equations into a quasilinear degenerate parabolic equation. In contrast to the Mises variables, the Crocco substitution allows one to study both stationary and nonstationary equations.
Keywords: symmetric boundary layer, O. A. Ladyzhenskaya's equations, Crocco transform, electrically conductive liquid. 
@article{INTO_2019_171_a1,
     author = {R. R. Bulatova},
     title = {O.~A.~Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {19--37},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a1/}
}
TY  - JOUR
AU  - R. R. Bulatova
TI  - O.~A.~Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 19
EP  - 37
VL  - 171
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_171_a1/
LA  - ru
ID  - INTO_2019_171_a1
ER  - 
%0 Journal Article
%A R. R. Bulatova
%T O.~A.~Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 19-37
%V 171
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_171_a1/
%G ru
%F INTO_2019_171_a1
R. R. Bulatova. O.~A.~Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 19-37. http://geodesic.mathdoc.fr/item/INTO_2019_171_a1/

[1] Bulatova R. R., Samokhin V. N., Chechkin G. A., “Uravneniya magnitogidrodinamicheskogo pogranichnogo sloya dlya modifitsirovannoi neszhimaemoi vyazkoi sredy. Otryv pogranichnogo sloya”, Probl. mat. anal., 92 (2018), 83–100 | Zbl

[2] Bulatova R. R., “Vliyanie magnitnogo polya na polozhenie tochki otryva pogranichnogo sloya elektroprovodnoi zhidkosti”, Izv. vuzov. Probl. poligrafii i izdat. dela., 2018, no. 1, 14–22

[3] Samokhin V. N., Fadeeva G. M., Chechkin G. A., “Uravneniya pogranichnogo sloya dlya modifitsirovannoi sistemy Nave—Stoksa”, Tr. semin. im. I. G. Petrovskogo, 28 (2011), 329–361 | Zbl

[4] 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

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

[6] Bulatova R. R., Chechkin G. A., Chechkina T. P., Samokhin V. N., “On the influence of a magnetic field on the separation of the boundary layer of a non-Newtonian MHD medium”, C. R. Méc., 346:9 (2018), 807–814 | DOI