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 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 Pra...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-06, Vol.263 (5), p.616-634
Main Author: Bulatova, R. R.
Format: Article
Language:English
Subjects:
Axioms
Boundary layer equations
Fluid flow
Incompressible flow
Mathematics
Mathematics and Statistics
Rheological properties
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05953-2