System of equations for boundary layer of rheologically complex media. The Crocco variables

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Abstract

In the paper one studies the system of equations of the boundary layer of nonlinearly viscous fluid with the O. A. Ladyzhenskaya law. Previously, these equations were considered, the Mises transform allows to reduce the system of equations to a single quasilinear equation. In this work, we use the Crocco variables, which transform the system of equations of the boundary layer into a quasilinear degenerate parabolic equation. In contrast to the Mises variables, the Crocco transformation allows one to study both stationary and non-stationary equations; moreover, it makes it possible to obtain asymptotic estimates for the solution on the boundary of the domain.

About the authors

R. R. Bulatova

Lomonosov Moscow State University

Author for correspondence.
Email: regina.bulatova@mech.math.msu.su
Russian Federation, 1, Leninskie gory, Moscow, 119991

V. N. Samokhin

Moscow Polytechnic University

Email: vnsamokhin@mtu-net.ru
Russian Federation, 38, B.Semenovskaya street, Moscow, 107023

G. A. Chechkin

Lomonosov Moscow State University; Institute of Mathematics with Computer Center of the Ufa Science Center of the Russian Academy of Sciences

Email: chechkin@mech.math.msu.su
Russian Federation, 1, Leninskie gory, Moscow, 119991; 112, Chernyshevskogo street, Ufa, 450008

References

  1. Самохин В. Н., Фадеева Г. М., Чечкин Г. А. Уравнения пограничного слоя для модифицированной системы Навье-Стокса // Тр. семинара им. И. Г. Петровского. 2011. Т. 28. С. 329-361.
  2. Самохин В. Н., Чечкин Г. А. Уравнения пограничного слоя обобщенно ньютоновской среды в окрестности критической точки // Тр. семинара им. И. Г. Петровского. 2016. Т. 31. С. 158-176.
  3. Булатова Р. Р., Самохин В. Н., Чечкин Г. А. Уравнения магнитогидродинамического пограничного слоя для модифицированной несжимаемой вязкой среды. Отрыв пограничного слоя // Пробл. мат. анализа. 2018. Т. 92. С. 83-100.
  4. 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 // CR Mécanique. 2018. V. 346. № 9. P. 807-814.
  5. Олейник О. А., Самохин В. Н. Математические методы в теории пограничного слоя. М.: Наука/Физматлит, 1997. 508 c.

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