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.
- incompressible viscoelastic polymeric medium
- Lyapunov stability
- magnetohydrodynamic flow
- Poiseuille-Type flow
- rheological relation