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Sbornik: Mathematics, 2020, Volume 211, Issue 7, Pages 901–921
DOI: https://doi.org/10.1070/SM9267 (Mi sm9267) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Stability of Poiseuille-type flows in an MHD model of an incompressible polymeric fluid

A. M. Blokhinab, D. L. Tkachevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
English version PDF (634 kB) Citations (11) Russian version article
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DOI: https://doi.org/10.1070/SM9267
Abstract: A generalization of the Pokrovskii-Vinogradov model for flows of solutions and melts of incompressible viscoelastic polymeric media to the case of nonisothermic flows in an infinite plane channel under the effect of a magnetic field is considered. A formal asymptotic representation is derived for the eigenvalues of the linearized problem (the basic solution is an analogue of the Poiseuille flow of a viscous fluid in the Navier-Stokes model) as their absolute value increases. A necessary condition for the asymptotic stability of an analogue of the Poiseuille shear flow is deduced.
Bibliography: 22 titles.
Keywords: incompressible viscoelastic polymeric medium, rheological relation, magnetohydrodynamic flow, Poiseuille-type flow, spectrum, Lyapunov stability.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00791-а
19-01-00261-а
This research was supported by the Russian Foundation for Basic Research (project nos. 17-01-00791-a and 19-01-00261-a).
Received: 18.04.2019 and 10.11.2019
Bibliographic databases:
Document Type: Article
UDC: 517.984.5+532.135
MSC: Primary 76A10; Secondary 35P15, 76E25
Language: English
Original paper language: Russian
Citation: A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows in an MHD model of an incompressible polymeric fluid”, Sb. Math., 211:7 (2020), 901–921
Citation in format AMSBIB
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\paper Stability of Poiseuille-type flows in an~MHD~model of an incompressible polymeric fluid
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\yr 2020
\vol 211
\issue 7
\pages 901--921
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    • This publication is cited in the following 11 articles:
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