Stability of Poiseuille-type Flows for an MHD Model of an Incompressible Polymeric Fluid

A new rheological model, an extension of the Pokrovskii-Vinogradov rheological model, describing the flows of melts and solutions of incompressible viscoelastic polymeric media in external uniform magnetic field in the presence of a temperature drop and conduction current is studied. An asymptotic representation of the linear problem spectrum resulting from the linearization of the initial boundary value problem in an infinite plane channel about a Poiseuille-type flow is obtained. For this Poiseuille-type flow the parameter domain of linear Lyapunov’s stability is determined.