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Sibirskii Zhurnal Industrial'noi Matematiki
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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 3, Pages 13–25 (Mi sjim842)  

This article is cited in 23 scientific papers (total in 23 papers)

Linear asymptotic instability of a stationary flow of a polymeric medium in a plane channel in the case of periodic perturbations

A. M. Blokhinab, D. L. Tkachevab

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
References:
Abstract: We study the linear stability of a stationary flow of an incompressible viscoelastic polymeric fluid in a plane infinite channel in the case of periodic perturbations with respect to a variable related to the length of the channel.
Keywords: polymer, rheological relation, stationary solution, Poiseuille flow, well-posedness, spectrum, Lyapunov stability.
Received: 11.03.2014
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 4, Pages 467–478
DOI: https://doi.org/10.1134/S1990478914040036
Bibliographic databases:
Document Type: Article
UDC: 517.958+517.956.3+539.3+544.275.7
Language: Russian
Citation: A. M. Blokhin, D. L. Tkachev, “Linear asymptotic instability of a stationary flow of a polymeric medium in a plane channel in the case of periodic perturbations”, Sib. Zh. Ind. Mat., 17:3 (2014), 13–25; J. Appl. Industr. Math., 8:4 (2014), 467–478
Citation in format AMSBIB
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\by A.~M.~Blokhin, D.~L.~Tkachev
\paper Linear asymptotic instability of a~stationary flow of a~polymeric medium in a~plane channel in the case of periodic perturbations
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 3
\pages 13--25
\mathnet{http://mi.mathnet.ru/sjim842}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364402}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 4
\pages 467--478
\crossref{https://doi.org/10.1134/S1990478914040036}
Linking options:
  • https://www.mathnet.ru/eng/sjim842
  • https://www.mathnet.ru/eng/sjim/v17/i3/p13
  • This publication is cited in the following 23 articles:
    1. Dmitry L. Tkachev, SEMA SIMAI Springer Series, 34, Hyperbolic Problems: Theory, Numerics, Applications. Volume I, 2024, 373  crossref
    2. D. L. Tkachev, A. V. Yegitov, E. A. Biberdorf, “Linear instability of a resting state of the magnetohydrodynamic flows of polymeric fluid in a cylindrical channel (generalized Vinogradov–Pokrovski model)”, Physics of Fluids, 36:9 (2024)  crossref
    3. D. L. Tkachev, “The spectrum and Lyapunov linear instability of the stationary state for polymer fluid flows: the Vinogradov–Pokrovskii model”, Siberian Math. J., 64:2 (2023), 407–423  mathnet  crossref  crossref
    4. D.L. Tkachev, “Spectrum and linear Lyapunov instability of a resting state for flows of an incompressible polymeric fluid”, Journal of Mathematical Analysis and Applications, 522:1 (2023), 126914  crossref
    5. Blokhin A.M., Tkachev D.L., Yegitov A.V., “Lyapunov Instability of the Stationary Flows of a Polymeric Fluid in An Infinite Plane Channel With Constant Flow Rate”, J. Math. Anal. Appl., 506:1 (2022), 125541  crossref  mathscinet  isi  scopus
    6. Blokhin A.M., Tkachev D.L., “Mhd Model of Incompressible Polymeric Fluid. Linear Instability of the Resting State”, Complex Var. Elliptic Equ., 66:6-7, SI (2021), 929–944  crossref  mathscinet  zmath  isi  scopus
    7. Blokhin A.M., Tkachev D.L., “Lyapunov Instability of the Stationary Flows of Polymeric Fluid With Constant Flow Rate”, ZAMM-Z. Angew. Math. Mech., 101:12 (2021), e202000384  crossref  mathscinet  isi  scopus
    8. Alexander Blokhin, Dmitry Tkachev, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2351, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2021, 040057  crossref
    9. A. M. Blokhin, A. S. Rudometova, D. L. Tkachev, “An MHD model of an incompressible polymeric fluid: linear instability of a steady state”, J. Appl. Industr. Math., 14:3 (2020), 430–442  mathnet  crossref  crossref  elib
    10. Blokhin A.M., Tkachev D.L., “Stability of the Poiseuille-Type Flow For a Mhd Model of An Incompressible Polymeric Fluid”, Eur. J. Mech. B-Fluids, 80 (2020), 112–121  crossref  mathscinet  zmath  isi  scopus
    11. A. M. Blokhin, D. L. Tkachev, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 45  crossref
    12. Alexander Blokhin, Dmitry Tkachev, “MHD model of an incompressible polymeric fluid. Linear instability of the resting state”, J. Phys.: Conf. Ser., 1666:1 (2020), 012007  crossref
    13. V. V. Privalova, E. Yu. Prosviryakov, M. A. Simonov, “Nonlinear Gradient Flow of a Vertical Vortex Fluid in a Thin Layer”, Rus. J. Nonlin. Dyn., 15:3 (2019), 271–283  mathnet  crossref  mathscinet
    14. A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows for an MHD model of an incompressible polymeric fluid”, J. Hyberbolic Differ. Equ., 16:4 (2019), 793–817  crossref  mathscinet  zmath  isi  scopus
    15. A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type flows for an MHD model of an incompressible polymeric fluid”, Fluid Dyn., 54:8 (2019), 1051–1058  crossref  crossref  isi  elib  scopus
    16. A. M. Blokhin, A. V. Yegitov, D. L. Tkachev, “Asymptotics of the spectrum of a linearized problem of the stability of a stationary flow of an incompressible polymer fluid with a space charge”, Comput. Math. Math. Phys., 58:1 (2018), 102–117  mathnet  crossref  crossref  isi  elib
    17. A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in an infinite channel”, J. Appl. Mech. Tech. Phys., 59:6 (2018), 992–1003  crossref  mathscinet  zmath  isi  scopus
    18. A. Blokhin, D. Tkachev, A. Yegitov, “Spectral asymptotics of a linearized problem for an incompressible weakly conducting polymeric fluid”, ZAMM-Z. Angew. Math. Mech., 98:4 (2018), 589–601  crossref  mathscinet  isi  scopus
    19. Alexander Blokhin, Dmitry Tkachev, AIP Conference Proceedings, 2027, 2018, 030028  crossref
    20. Aleksey Yegitov, AIP Conference Proceedings, 2027, 2018, 040003  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский журнал индустриальной математики
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