MHD model of an 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).