Spectrum and linear Lyapunov instability of a resting state for flows of an incompressible polymeric fluid

The Lyapunov linear instability of the state of rest for flows of an incompressible viscoelastic polymeric fluid in an infinite plane channel is proved. We use the Vinogradov-Pokrovski rheological model, which is well suited for describing the flow characteristics of linear polymer melts. The spectrum of the mixed problem is found and it is proved that the solution of a linearized mixed problem in the class of periodic perturbations with respect to a variable varying along the channel wall grows in time faster than any exponential function to a linear degree. (c) 2022 Elsevier Inc. All rights reserved.