Abstract:
The rheological Pokrovskii-Vinogradov model for flows of solutions or melts of an incompressible viscoelastic polymeric medium is studied in the case of flows in an infinite planar channel with perforated walls. The linear Lyapunov instability is proved for the base solution with constant flow rate in the class of perturbations periodic in the variable varying along the channel wall.
Bibliography: 14 titles.
Keywords:
incompressible viscoelastic polymeric medium, rheological relation, infinite planar channel with perforated walls, base solution, linear Lyapunov instability.
This study was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project no. FWNF-2022-0008) and also was supported by the Russian Foundation for Basic Research (grant no. 19-01-00261-а).
Citation:
A. M. Blokhin, D. L. Tkachev, “Lyapunov instability of stationary flows of a polymeric fluid in a channel with perforated walls”, Sb. Math., 213:3 (2022), 283–299
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\by A.~M.~Blokhin, D.~L.~Tkachev
\paper Lyapunov instability of stationary flows of a~polymeric fluid in a~channel with perforated walls
\jour Sb. Math.
\yr 2022
\vol 213
\issue 3
\pages 283--299
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Linking options:
https://www.mathnet.ru/eng/sm9507
https://doi.org/10.1070/SM9507
https://www.mathnet.ru/eng/sm/v213/i3/p3
This publication is cited in the following 3 articles:
Dmitry L. Tkachev, SEMA SIMAI Springer Series, 34, Hyperbolic Problems: Theory, Numerics, Applications. Volume I, 2024, 373
B. V. Semisalov, “Exact Poiseuil-type solutions for flows of viscoelastic polymer fluid through a circular pipe”, J. Appl. Mech. Tech. Phys., 64:4 (2023), 675–685
B. V. Semisalov, “On a scenario of transition to turbulence for polymer fluid flow in a circular pipe”, Math. Models Comput. Simul., 16:2 (2024), 197–207
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