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

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

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2020, Volume: 14, Number: 3, Pages: 430-442 Pages count : 13 DOI: 10.1134/S1990478920030035

Tags

incompressible viscoelastic polymeric fluid; Lyapunov stability; magnetohydrodynamic flow; Poiseuille-type flow; rheological correlation; spectrum; steady state

Authors

Blokhin A.M. ^1,2 , Rudometova A.S. ^1,2 , Tkachev D.L. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation

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).

Blokhin A.M. , Rudometova A.S. , Tkachev D.L.
An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State
Journal of Applied and Industrial Mathematics. 2020. V.14. N3. P.430-442. DOI: 10.1134/S1990478920030035 Scopus OpenAlex

Блохин А.М. , Рудометова А.С. , Ткачев Д.Л.
МГД модель несжимаемой полимерной жидкости: линейная неустойчивость состояния покоя
Сибирский журнал индустриальной математики. 2020. Т.23. №3. С.16–30.

Scopus:	2-s2.0-85094676365
OpenAlex:	W3096159654

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