Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in the infinite channel

A new rheological model (a modification of the Pokrovskii–Vinogradov model) is investigated. The model was shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with a complex geometry of the boundary. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity on the variable that runs along the axis of the channel.