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.

N1 - Publisher Copyright: © 2020 Russian Academy of Sciences (DoM) and London Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

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 -