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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ACKNOWLEDGMENTS
The authors are grateful to A. V. Yegitov for help in designing the manuscript.
Funding
The authors were supported by the Russian Foundation for Basic Research (project no. 19–01–00261) and the Siberian Branch of the Russian Academy of Sciences (the Program of Basic Research No. I.1.5, project 0314–2019–0013).
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Translated by G.A. Chumakov
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Blokhin, A.M., Rudometova, A.S. & Tkachev, D.L. An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State. J. Appl. Ind. Math. 14, 430–442 (2020). https://doi.org/10.1134/S1990478920030035
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DOI: https://doi.org/10.1134/S1990478920030035