The Spectrum and Lyapunov Linear Instability of the Stationary State for Polymer Fluid Flows:The Vinogradov–Pokrovskii Model Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
||
|---|---|---|---|
| Output data | Year: 2023, Volume: 64, Number: 2, Pages: 407-423 Pages count : 17 DOI: 10.1134/s0037446623020131 | ||
| Tags | incompressible viscoelastic polymer medium, rheological relation, stationary state, linearized mixed problem, Lyapunov stability | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0008 |
Abstract:
We study the Lyapunov linear stability of the stationary state for flows of an incompressible viscoelastic polymer fluid in an infinite planar channel. As a model we choose the Vinogradov–Pokrovskii rheological model well-suited for describing the flow characteristics of linear polymer melts. We find the spectrum of the mixed problem and prove that the solution to the linearized mixed problem in the class of periodic perturbations of the variable changing along the channel side grows faster in time than the exponential with a linear exponent. In other words, the stationary state is linearly unstable.
Cite:
Tkachev D.L.
The Spectrum and Lyapunov Linear Instability of the Stationary State for Polymer Fluid Flows:The Vinogradov–Pokrovskii Model
Siberian Mathematical Journal. 2023. V.64. N2. P.407-423. DOI: 10.1134/s0037446623020131 WOS Scopus РИНЦ OpenAlex
The Spectrum and Lyapunov Linear Instability of the Stationary State for Polymer Fluid Flows:The Vinogradov–Pokrovskii Model
Siberian Mathematical Journal. 2023. V.64. N2. P.407-423. DOI: 10.1134/s0037446623020131 WOS Scopus РИНЦ OpenAlex
Original:
Ткачев Д.Л.
Спектр и линейная неустойчивость по Ляпунову состояния покоя для течений полимерной жидкости (модель Виноградова — Покровского)
Сибирский математический журнал. 2023. Т.64. №2. С.423–440. DOI: 10.33048/smzh.2023.64.213 РИНЦ
Спектр и линейная неустойчивость по Ляпунову состояния покоя для течений полимерной жидкости (модель Виноградова — Покровского)
Сибирский математический журнал. 2023. Т.64. №2. С.423–440. DOI: 10.33048/smzh.2023.64.213 РИНЦ
Dates:
| Submitted: | Apr 1, 2022 |
| Accepted: | Jan 10, 2023 |
| Published print: | Mar 24, 2023 |
| Published online: | Mar 24, 2023 |
Identifiers:
| Web of science: | WOS:000984262300013 |
| Scopus: | 2-s2.0-85151069056 |
| Elibrary: | 61123490 |
| OpenAlex: | W4360831367 |