Nonclassical problems in mathematical hydrodynamics arise when studying the motion of rheologically complex media, as well as under boundary conditions different from classical ones. In this paper, existence and uniqueness theorems are established for the classical solution to the problem of a stationary boundary layer of a liquid with the rheological law of Ladyzhenskaya near a solid wall with given conditions characterizing the force of surface tension and the phenomenon of slipping near this wall.

An Erratum to this paper has been published: https://doi.org/10.1134/S1064562422340026

An existence and uniqueness theorem for a classical solution to the system of equations describing thermal boundary layers in viscous media with the Ladyzhenskaya rheological law is generalized.

We establish the existence and uniqueness of the classical solution to the system of magnetohydrodynamic boundary layer equations in a viscous medium with an injection of a modified medium obeying the Ladyzhenskaya rheological law.

One considers flow past a body in an electrically conductive viscous fluid in magnetic field, the fluid being subject to a nonlinear rheological law. Solutions of the corresponding system of magnetohydrodynamic boundary layer are examined in a neighborhood of a frontal critical point.

We consider a nonstationary Prandtl-type system of equations that describes the behavior of a boundary layer of a viscous incompressible fluid in the modification of O. A. Ladyzhenskaya. We prove an existence and uniqueness theorem both in Cartesian coordinates and in terms of the Crocco variables.

The unique solvability of the problem for the equations governing a nonstationary boundary layer of a viscous fluid subject to the Ladyzhenskaya rheological law is studied in the literature for the first time. We prove the existence and uniqueness of a solution to the problem. Bibliography: 7 titles.

We consider the system of boundary layer equations governing a viscous medium subject to the nonlinear rheological law in the sense of Ladyzhenskaya. Owing to the use of the Crocco transformation for reducing the system to a single quasilinear equation, it becomes possible to study both stationary and nonstationary boundary layers. We obtain asymptotic estimates for the solution.

The system of boundary-layer equations for a nonlinear generalized Newtonian viscous fluid with the Ladyzhenskaya law is studied. The correct solvability of the problem under study is proved using the Crocco transformation method, which reduces the system of boundary-layer equations to a quasilinear degenerate parabolic equation. Asymptotic estimates for the solution on the boundary of the domain are obtained.

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.

Изучается система уравнений пограничного слоя нелинейной обобщённо-ньютоновской вязкой жидкости, модификацию которой предложила О.А. Ладыженская. Для доказательства корректной разрешимости поставленной задачи в работе применяется метод преобразования Крокко, который переводит систему пограничного слоя в одно квазилинейное вырождающееся параболическое уравнение. Получены асимптотические оценки решения на границе области.

We study the behavior of a magnetohydrodynamic (MHD) stationary boundary layer in a framework modified according to O.A. Ladyzhenskaya. We estimate the shift of a separation point under the influence of a magnetic field. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

We study the behavior of a magnetohydrodynamic stationary boundary layer of a modified fluid in the sense of Ladyzhenskaya. We study how a magneric force affects the behavior of a continuous medium. We establish the influence of the magnetic field on the point of separation of the boundary layer from the solid streamlined surface.

We consider a model of flow past a body in a viscous continuous medium with a nonlinear rheologic law and study the problem of continuation of boundary layer.