O. A. Ladyzhenskaya's system of equations of symmetric boundary layer of modified fluid

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.