Standard

An MHD Model of an Incompressible Polymeric Fluid : Linear Instability of a Steady State. / Blokhin, A. M.; Rudometova, A. S.; Tkachev, D. L.

In: Journal of Applied and Industrial Mathematics, Vol. 14, No. 3, 01.08.2020, p. 430-442.

Research output: Contribution to journal › Article › peer-review

Harvard

Blokhin, AM, Rudometova, AS & Tkachev, DL 2020, 'An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State', Journal of Applied and Industrial Mathematics, vol. 14, no. 3, pp. 430-442. https://doi.org/10.1134/S1990478920030035

APA

Blokhin, A. M., Rudometova, A. S., & Tkachev, D. L. (2020). An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State. Journal of Applied and Industrial Mathematics, 14(3), 430-442. https://doi.org/10.1134/S1990478920030035

Vancouver

Blokhin AM, Rudometova AS, Tkachev DL. An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State. Journal of Applied and Industrial Mathematics. 2020 Aug 1;14(3):430-442. doi: 10.1134/S1990478920030035

Author

Blokhin, A. M. ; Rudometova, A. S. ; Tkachev, D. L. / An MHD Model of an Incompressible Polymeric Fluid : Linear Instability of a Steady State. In: Journal of Applied and Industrial Mathematics. 2020 ; Vol. 14, No. 3. pp. 430-442.

BibTeX

@article{823e9b1f856d4b6e86f9e14091b2fd73,
title = "An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State",
abstract = "Abstract: We study linear stability of a steady state for a generalization of the basic rheologicalPokrovskii–Vinogradov model which describes the flows of melts and solutions of anincompressible viscoelastic polymeric medium in the nonisothermal case under the influence ofa magnetic field. We prove that the corresponding linearized problem describingmagnetohydrodynamic 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 channelboundaries), there exist solutions whose amplitude grows exponentially (in the class of functionsperiodic along the channel).",
keywords = "incompressible viscoelastic polymeric fluid, Lyapunov stability, magnetohydrodynamic flow, Poiseuille-type flow, rheological correlation, spectrum, steady state",
author = "Blokhin, {A. M.} and Rudometova, {A. S.} and Tkachev, {D. L.}",
year = "2020",
month = aug,
day = "1",
doi = "10.1134/S1990478920030035",
language = "English",
volume = "14",
pages = "430--442",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - An MHD Model of an Incompressible Polymeric Fluid

T2 - Linear Instability of a Steady State

AU - Blokhin, A. M.

AU - Rudometova, A. S.

AU - Tkachev, D. L.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - Abstract: We study linear stability of a steady state for a generalization of the basic rheologicalPokrovskii–Vinogradov model which describes the flows of melts and solutions of anincompressible viscoelastic polymeric medium in the nonisothermal case under the influence ofa magnetic field. We prove that the corresponding linearized problem describingmagnetohydrodynamic 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 channelboundaries), there exist solutions whose amplitude grows exponentially (in the class of functionsperiodic along the channel).

AB - Abstract: We study linear stability of a steady state for a generalization of the basic rheologicalPokrovskii–Vinogradov model which describes the flows of melts and solutions of anincompressible viscoelastic polymeric medium in the nonisothermal case under the influence ofa magnetic field. We prove that the corresponding linearized problem describingmagnetohydrodynamic 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 channelboundaries), there exist solutions whose amplitude grows exponentially (in the class of functionsperiodic along the channel).

KW - incompressible viscoelastic polymeric fluid

KW - Lyapunov stability

KW - magnetohydrodynamic flow

KW - Poiseuille-type flow

KW - rheological correlation

KW - spectrum

KW - steady state

UR - http://www.scopus.com/inward/record.url?scp=85094676365&partnerID=8YFLogxK

U2 - 10.1134/S1990478920030035

DO - 10.1134/S1990478920030035

M3 - Article

AN - SCOPUS:85094676365

VL - 14

SP - 430

EP - 442

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -

ID: 25865480