MHD model of incompressible polymeric fluid. Linear instability of the resting state

Standard

MHD model of incompressible polymeric fluid. Linear instability of the resting state. / Blokhin, A. M.; Tkachev, D. L.

In: Complex Variables and Elliptic Equations, Vol. 66, No. 6-7, 2021, p. 929-944.

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

Harvard

Blokhin, AM & Tkachev, DL 2021, 'MHD model of incompressible polymeric fluid. Linear instability of the resting state', Complex Variables and Elliptic Equations, vol. 66, no. 6-7, pp. 929-944. https://doi.org/10.1080/17476933.2020.1797706

APA

Blokhin, A. M., & Tkachev, D. L. (2021). MHD model of incompressible polymeric fluid. Linear instability of the resting state. Complex Variables and Elliptic Equations, 66(6-7), 929-944. https://doi.org/10.1080/17476933.2020.1797706

Vancouver

Blokhin AM, Tkachev DL. MHD model of incompressible polymeric fluid. Linear instability of the resting state. Complex Variables and Elliptic Equations. 2021;66(6-7):929-944. doi: 10.1080/17476933.2020.1797706

Author

Blokhin, A. M. ; Tkachev, D. L. / MHD model of incompressible polymeric fluid. Linear instability of the resting state. In: Complex Variables and Elliptic Equations. 2021 ; Vol. 66, No. 6-7. pp. 929-944.

BibTeX

@article{7eaf8fbd077f44db91b4a35f09d806e8,

title = "MHD model of incompressible polymeric fluid. Linear instability of the resting state",

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

keywords = "76A05, 76E25, Incompressible viscoelastic polymeric medium, Lyapunov's stability, magnetohydrodynamic flow, resting state, rheological relation, spectrum, STABILITY, ASYMPTOTICS, FLOWS, SPECTRUM",

author = "Blokhin, {A. M.} and Tkachev, {D. L.}",

year = "2021",

doi = "10.1080/17476933.2020.1797706",

language = "English",

volume = "66",

pages = "929--944",

journal = "Complex Variables and Elliptic Equations",

issn = "1747-6933",

publisher = "Taylor and Francis Ltd.",

number = "6-7",

}

RIS

TY - JOUR

T1 - MHD model of incompressible polymeric fluid. Linear instability of the resting state

AU - Blokhin, A. M.

AU - Tkachev, D. L.

PY - 2021

Y1 - 2021

N2 - We study the linear stability of a resting state for a generalization of the basic rheological Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to the nonisothermal case under the influence of magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: for certain values of the conduction current which is given on the electrodes, i.e. on the channel boundaries, the problem has solutions whose amplitude grows exponentially (in the class of functions periodic along the channel).

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

KW - 76A05

KW - 76E25

KW - Incompressible viscoelastic polymeric medium

KW - Lyapunov's stability

KW - magnetohydrodynamic flow

KW - resting state

KW - rheological relation

KW - spectrum

KW - STABILITY

KW - ASYMPTOTICS

KW - FLOWS

KW - SPECTRUM

UR - http://www.scopus.com/inward/record.url?scp=85089473697&partnerID=8YFLogxK

U2 - 10.1080/17476933.2020.1797706

DO - 10.1080/17476933.2020.1797706

M3 - Article

AN - SCOPUS:85089473697

VL - 66

SP - 929

EP - 944

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 6-7

ER -

ID: 25298090