Stability of Poiseuille-Type flows in an MHD model of an incompressible polymeric fluid

Standard

Stability of Poiseuille-Type flows in an MHD model of an incompressible polymeric fluid. / Blokhin, A. M.; Tkachev, D. L.

In: Sbornik Mathematics, Vol. 211, No. 7, 07.2020, p. 901-921.

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

BibTeX

@article{c62d257356854ce2820df98272a5d605,

title = "Stability of Poiseuille-Type flows in an MHD model of an incompressible polymeric fluid",

abstract = "A generalization of the Pokrovskii-Vinogradov model for flows of solutions and melts of incompressible viscoelastic polymeric media to the case of nonisothermic flows in an infinite plane channel under the effect of a magnetic field is considered. A formal asymptotic representation is derived for the eigenvalues of the linearized problem (the basic solution is an analogue of the Poiseuille flow of a viscous fluid in the Navier-Stokes model) as their absolute value increases. A necessary condition for the asymptotic stability of an analogue of the Poiseuille shear flow is deduced. Bibliography: 22 titles.",

keywords = "incompressible viscoelastic polymeric medium, Lyapunov stability, magnetohydrodynamic flow, Poiseuille-Type flow, rheological relation, spectrum",

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

year = "2020",

month = jul,

doi = "10.1070/SM9267",

language = "English",

volume = "211",

pages = "901--921",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "7",

}

RIS

TY - JOUR

T1 - Stability of Poiseuille-Type flows in an MHD model of an incompressible polymeric fluid

AU - Blokhin, A. M.

AU - Tkachev, D. L.

PY - 2020/7

Y1 - 2020/7

N2 - A generalization of the Pokrovskii-Vinogradov model for flows of solutions and melts of incompressible viscoelastic polymeric media to the case of nonisothermic flows in an infinite plane channel under the effect of a magnetic field is considered. A formal asymptotic representation is derived for the eigenvalues of the linearized problem (the basic solution is an analogue of the Poiseuille flow of a viscous fluid in the Navier-Stokes model) as their absolute value increases. A necessary condition for the asymptotic stability of an analogue of the Poiseuille shear flow is deduced. Bibliography: 22 titles.

AB - A generalization of the Pokrovskii-Vinogradov model for flows of solutions and melts of incompressible viscoelastic polymeric media to the case of nonisothermic flows in an infinite plane channel under the effect of a magnetic field is considered. A formal asymptotic representation is derived for the eigenvalues of the linearized problem (the basic solution is an analogue of the Poiseuille flow of a viscous fluid in the Navier-Stokes model) as their absolute value increases. A necessary condition for the asymptotic stability of an analogue of the Poiseuille shear flow is deduced. Bibliography: 22 titles.

KW - incompressible viscoelastic polymeric medium

KW - Lyapunov stability

KW - magnetohydrodynamic flow

KW - Poiseuille-Type flow

KW - rheological relation

KW - spectrum

UR - http://www.scopus.com/inward/record.url?scp=85092055735&partnerID=8YFLogxK

U2 - 10.1070/SM9267

DO - 10.1070/SM9267

M3 - Article

AN - SCOPUS:85092055735

VL - 211

SP - 901

EP - 921

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 7

ER -

ID: 26155589