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Contemporary Mathematics. Fundamental Directions, 2003, Volume 2, Pages 57–69 (Mi cmfd21)  

This article is cited in 8 scientific papers (total in 8 papers)

On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids

V. G. Zvyagin

Voronezh State University
Full-text PDF (211 kB) Citations (8)
References:
Abstract: In the paper, the settings of initial-boundary and initial value problems arising in a number of models of movement of nonlinearly viscous or viscoelastic incompressible fluid are considered, and existence theorems for these problems are presented. In particular, the settings of initial-boundary value problems appearing in the regularized model of the movement of viscoelastic fluid with Jeffris constitutive relation are described. The theorems for the existence of weak and strong solutions for these problems in bounded domains are given. The initial value problem for a nonlinearly viscous fluid on the whole space is considered. The estimates on the right-hand side and initial conditions under which there exist local and global solutions of this problem are presented. The modification of Litvinov's model for laminar and turbulent flows with a memory is described. The existence theorem for weak solutions of initial-boundary value problem appearing in this model is given.
English version:
Journal of Mathematical Sciences, 2004, Volume 124, Issue 5, Pages 5321–5334
DOI: https://doi.org/10.1023/B:JOTH.0000047357.93280.18
Bibliographic databases:
UDC: 517.95+517.958
Language: Russian
Citation: V. G. Zvyagin, “On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 2, CMFD, 2, MAI, M., 2003, 57–69; Journal of Mathematical Sciences, 124:5 (2004), 5321–5334
Citation in format AMSBIB
\Bibitem{Zvy03}
\by V.~G.~Zvyagin
\paper On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids
\inbook Proceedings of the International Conference on Differential and Functional-Differential Equations --- Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11--17 August, 2002). Part~2
\serial CMFD
\yr 2003
\vol 2
\pages 57--69
\publ MAI
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd21}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2129135}
\zmath{https://zbmath.org/?q=an:1128.76319}
\transl
\jour Journal of Mathematical Sciences
\yr 2004
\vol 124
\issue 5
\pages 5321--5334
\crossref{https://doi.org/10.1023/B:JOTH.0000047357.93280.18}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :147
    References:42
     
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