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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2019, Volume 12, Issue 3, Pages 42–51
DOI: https://doi.org/10.14529/mmp190304
(Mi vyuru503)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Modelling

A non-stationary model of the incompressible viscoelastic Kelvin–Voigt fluid of non-zero order in the magnetic field of the Earth

A. O. Kondyukova, T. G. Sukachevaab

a Novgorod State University, Velikiy Novgorod, Russian Federation
b South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (231 kB) Citations (2)
References:
Abstract: We investigate the Cauchy–Dirichlet problem for a system of Oskolkov equations of nonzero order. The considered mathematical model describes the flow of an incompressible viscoelastic Kelvin–Voigt fluid in the magnetic field of the Earth. The model takes into account that the fluid is subject to various external influences, which depend on both the coordinate of the point in space and the time. The first part of the paper presents the known results obtained by the authors earlier and based on the theory of solvability of the Cauchy problem for semilinear nonautonomous Sobolev type equations. In the second part, we reduce the considered mathematical model to an abstract Cauchy problem. In the third part, we prove the main result that is the theorem on the existence and uniqueness of the solution. Also, we establish the conditions for the existence of quasi-stationary semitrajectories, and describe the extended phase space of the model under study. In this paper, we summarize our results for the Oskolkov system that simulates the motion of a viscoelastic incompressible Kelvin–Voigt fluid of zero order in the magnetic field of the Earth.
Keywords: magnetohydrodynamics, Sobolev type equations, extended phase space, incompressible viscoelastic fluid.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
The work was supported by the Government of the Russian Federation (act 211, contract no. 02.A03.21.0011).
Received: 21.04.2019
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35G61
Language: English
Citation: A. O. Kondyukov, T. G. Sukacheva, “A non-stationary model of the incompressible viscoelastic Kelvin–Voigt fluid of non-zero order in the magnetic field of the Earth”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:3 (2019), 42–51
Citation in format AMSBIB
\Bibitem{KonSuk19}
\by A.~O.~Kondyukov, T.~G.~Sukacheva
\paper A non-stationary model of the incompressible viscoelastic Kelvin--Voigt fluid of non-zero order in the magnetic field of the Earth
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2019
\vol 12
\issue 3
\pages 42--51
\mathnet{http://mi.mathnet.ru/vyuru503}
\crossref{https://doi.org/10.14529/mmp190304}
\elib{https://elibrary.ru/item.asp?id=41265002}
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  • https://www.mathnet.ru/eng/vyuru503
  • https://www.mathnet.ru/eng/vyuru/v12/i3/p42
  • This publication is cited in the following 2 articles:
    1. Sangamesh, K. R. Raghunatha, I. S. Shivakumara, “Instability of double-diffusive magnetoconvection in a non-Newtonian fluid layer with cross-diffusion effects”, Physics of Fluids, 36:8 (2024)  crossref
    2. T. G. Sukacheva, “Modeli Oskolkova i uravneniya sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:1 (2022), 5–22  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
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