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Linear instability of a resting state for flows of polymeric fluid in cylinder channel (Vinogradov-Pokrovski model) Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2025,
Tags incompressible viscoelastic polymeric medium, rheological correlation, resting state, linearized mixed problem, Lyapunov stability.
Authors Tkachev D.L. 1 , Biberdorf E.A. 1
Affiliations
1 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0008

Abstract: 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 equiation 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.
Cite: Tkachev D.L. , Biberdorf E.A.
Linear instability of a resting state for flows of polymeric fluid in cylinder channel (Vinogradov-Pokrovski model)
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025.
Dates:
Submitted: Nov 5, 2025
Accepted: Dec 5, 2025
Identifiers: No identifiers
Citing: Пока нет цитирований