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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 845–870 (Mi zvmmf10038)  

This article is cited in 13 scientific papers (total in 13 papers)

Stationary solutions of equations of incompressible viscoelastic polymer liquid

N. V. Bambaevaa, A. M. Blokhinba

a Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
b Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: The equations describing flows of an incompressible viscoelastic polymer liquid are studied. Stationary solutions similar to the Poiseuille and Couette solutions for the system of the Navier–Stokes equations are constructed. Stationary discontinuous solutions of the polymer liquid equation are also considered.

Key words: polymer medium, steady flows, stationary discontinuous solutions, Poiseuille and Couette solutions, Navier–Stokes equations.

DOI: https://doi.org/10.7868/S0044466914050068

Full text: PDF file (414 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 845–870

Bibliographic databases:

UDC: 519.634
Received: 16.10.2012

Citation: N. V. Bambaeva, A. M. Blokhin, “Stationary solutions of equations of incompressible viscoelastic polymer liquid”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 845–870; Comput. Math. Math. Phys., 54:5 (2014), 845–870

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Blokhin, B. V. Semisalov, “A stationary flow of an incompressible viscoelastic polymeric fluid through a channel with elliptical cross section”, J. Appl. Industr. Math., 9:1 (2015), 18–26  mathnet  crossref  mathscinet
    2. A. M. Blokhin, A. S. Rudometova, “Stationary solutions to the equations describing the nonisothermic electrical convection of a weak-conductive incompressible polymeric fluid”, J. Appl. Industr. Math., 9:2 (2015), 147–156  mathnet  crossref  crossref  mathscinet  elib
    3. A. M. Blokhin, B. V. Semisalov, A. S. Shevchenko, “Statsionarnye resheniya uravnenii, opisyvayuschikh neizotermicheskie techeniya neszhimaemoi vyazkouprugoi polimernoi zhidkosti”, Matem. modelirovanie, 28:10 (2016), 3–22  mathnet  elib
    4. A. M. Blokhin, A. Yu. Goldin, “On linear stability of an incompressible polymer liquid at rest”, J. Math. Sci., 230:1 (2018), 14–24  mathnet  crossref  crossref
    5. A. Yegitov, “Asymptotic representation for spectrum of linear problem describing flows of viscoelastic polymeric fluid”, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, eds. A. Chesnokov, E. Pruuel, V. Shelukhin, IOP Publishing Ltd, 2017, UNSP 012138  crossref  isi  scopus
    6. A. M. Blokhin, R. E. Semenko, “Stationary electrohydrodynamic flows of incompressible polymeric media with strong discontinuity”, J. Math. Sci., 231:2 (2018), 143–152  mathnet  crossref  crossref
    7. A. M. Blokhin, R. E. Semenko, “Incompressible polymer fluid flow past a flat wedge”, J. Appl. Mech. Tech. Phys., 59:1 (2018), 32–40  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. A. M. Blokhin, A. Yu. Goldin, “On the linear instability of incompressible polymeric liquid flows with strong discontinuity”, Tech. Phys., 63:10 (2018), 1459–1467  crossref  isi  scopus
    10. A. M. Blokhin, A. Yu. Goldin, “Vyvod lineinoi i nelineinoi akusticheskikh sistem dlya neszhimaemoi vyazkouprugoi polimernoi zhidkosti”, Sib. zhurn. industr. matem., 23:1 (2020), 16–27  mathnet  crossref
    11. A. M. Blokhin, R. E. Semenko, “Vikhrevye statsionarnye struktury Karmana v magnitogidrodinamicheskikh techeniyakh vraschayuscheisya neszhimaemoi polimernoi zhidkosti”, Matem. modelirovanie, 32:7 (2020), 3–23  mathnet  crossref
    12. A. M. Blokhin, D. L. Tkachev, “Lineinaya neustoichivost sostoyaniya pokoya dlya MGD modeli neszhimaemoi polimernoi zhidkosti v sluchae absolyutnoi provodimosti”, Matem. tr., 24:1 (2021), 35–51  mathnet  crossref
    13. A. M. Blokhin, R. E. Semenko, A. S. Rudometova, “Magnetohydrodynamic vortex motion of an incompressible polymeric fluid”, J. Appl. Industr. Math., 15:1 (2021), 7–16  mathnet  crossref  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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