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O. A. Ladyzhenskaya’s System of Equations of Symmetric Boundary Layer of Modified Fluid

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Abstract

In this paper, we study the system of equations of a boundary layer for a nonlinearly viscous, electrically conductive liquid 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.

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References

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    R. R. Bulatova

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  1. R. R. Bulatova
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Correspondence to R. R. Bulatova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 171, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 2, 2019.

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Bulatova, R.R. O. A. Ladyzhenskaya’s System of Equations of Symmetric Boundary Layer of Modified Fluid. J Math Sci 263, 616–634 (2022). https://doi.org/10.1007/s10958-022-05953-2

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  • DOI: https://doi.org/10.1007/s10958-022-05953-2

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