Аннотация:

We study the linear stability of a resting state for flows of incompressible viscoelastic polymeric fluid in an infinite cylindrical channel in axisymmetric perturbation class. We use structurally-phenomenological Vinogradov-Pokrovski model as our mathematical model.

We state several  analytically equivalent spectral problems: two for equation systems and another two for high-order equations we can get from them. Our numerical experiments show that with the growth of perturbations frequency along the channel axis there appear eigenvalues with positive real part. Moreover it turns out that one of the problems for the system gives more accurate results. That guarantees linear Lyapunov instability of the resting state.