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This article is cited in 1 scientific paper (total in 1 paper)
Differential Equations and Mathematical Physics
On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
A. A. Domnicha, E. S. Baranovskiib, M. A. Artemovb a Russian Air Force Military Educational and Scientific Center of the "N. E. Zhukovskiy and Yu. A. Gagarin Air Force Academy", Voronezh, 394064, Russian Federation
b Voronezh State University, Voronezh, 394018, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
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.
Keywords:
flux problem, non-isothermal flows, creeping flows, mixed boundary conditions, weak solutions.
Received: June 15, 2019 Revised: July 14, 2019 Accepted: September 16, 2019 First online: October 14, 2019
Citation:
A. A. Domnich, E. S. Baranovskii, M. A. Artemov, “On a mathematical model of non-isothermal creeping flows of a fluid through a given domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:3 (2019), 417–429
Linking options:
https://www.mathnet.ru/eng/vsgtu1713 https://www.mathnet.ru/eng/vsgtu/v223/i3/p417
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