Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in the Infinite Channel
A. M. Blokhin1,2, D. L. Tkachev1,2, A. V. Egitov1,2
1Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University
Keywords: реологическая модель, полимерная среда, течение типа течения Пуазейля, устойчивость по Ляпунову, rheological model, polymer medium, flow type Poiseuille flows, Lyapunov stability
Abstract
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.
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