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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2019, Volume 23, Number 3, Pages 417–429
DOI: https://doi.org/10.14498/vsgtu1713
(Mi vsgtu1713)
 

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
Full-text PDF (977 kB) Citations (1)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
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
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.32
MSC: 35Q35, 35Q79, 35A01
Language: Russian
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
Citation in format AMSBIB
\Bibitem{DomBarArt19}
\by A.~A.~Domnich, E.~S.~Baranovskii, M.~A.~Artemov
\paper On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 3
\pages 417--429
\mathnet{http://mi.mathnet.ru/vsgtu1713}
\crossref{https://doi.org/10.14498/vsgtu1713}
\elib{https://elibrary.ru/item.asp?id=41801504}
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  • https://www.mathnet.ru/eng/vsgtu/v223/i3/p417
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Abstract page:594
    Full-text PDF :284
    References:41
     
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