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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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