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An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State

Authors
  • Blokhin, A. M.1, 2
  • Rudometova, A. S.1, 2
  • Tkachev, D. L.1, 2
  • 1 Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
  • 2 Novosibirsk State University, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
Type
Published Article
Journal
Journal of Applied and Industrial Mathematics
Publisher
Pleiades Publishing
Publication Date
Aug 01, 2020
Volume
14
Issue
3
Pages
430–442
Identifiers
DOI: 10.1134/S1990478920030035
Source
Springer Nature
Keywords
License
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Abstract

Abstract We study linear stability of a steady state for a generalization of the basic rheological Pokrovskii–Vinogradov model which describes the flows of melts and solutions of an incompressible viscoelastic polymeric medium in the nonisothermal case under the influence of a magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: For some values of the conduction current which is given on the electrodes (i.e. at the channel boundaries), there exist solutions whose amplitude grows exponentially (in the class of functions periodic along the channel).

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