On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity

Abstract

We study linear stability of steady states for a certain generalization (namely, nonisothermal flows under the influence of magnetic field) of the Pokrovskiĭ–Vinogradov basic rheological model which describes flows of solutions and melts of incompressible viscoelastic polymeric media. We prove that the linear problem describing magnetohydrodynamic (MHD) flow of polymers in an infinite plane channel has the following property: For a certain behavior of magnetic field outside of the channel, there exists a solution of the problem whose amplitude grows exponentially (in the class of functions that are periodic with respect to the variable changing along the side of the channel).