On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
We study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Samara State Technical University
2019-09-01
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Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
Subjects: | |
Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20621/16868 |
Summary: | We study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions. On in-flow and out-flow parts of the boundary the pressure, the temperature and the tangential component of the velocity field are prescribed, while on impermeable solid walls the no-slip condition and a Robin-type condition for the temperature are used. For this boundary-value problem, we introduce the concept of a weak solution (a pair “velocity-temperature”), which is defined as a solution to some system of integral equations. The main result of the work is a theorem on the existence of weak solutions in a subspace of the Cartesian product of two Sobolev's spaces. To prove this theorem, we give an operator interpretation of the boundary value problem, derive a priori estimates of solutions, and apply the Leray-Schauder fixed point theorem. Moreover, energy equalities are established for weak solutions. |
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ISSN: | 1991-8615 2310-7081 |