An MHD Model of an Incompressible Polymeric Fluid: Linear Instability of a Steady State

Abstract: We study linear stability of a steady state for a generalization of the basic rheologicalPokrovskii–Vinogradov model which describes the flows of melts and solutions of anincompressible viscoelastic polymeric medium in the nonisothermal case under the influence ofa magnetic field. We prove that the corresponding linearized problem describingmagnetohydrodynamic flows of polymers in an infinite plane channel has the following property:For some values of the conduction current which is given on the electrodes (i.e. at the channelboundaries), there exist solutions whose amplitude grows exponentially (in the class of functionsperiodic along the channel).