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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 6, Pages 1338–1353 (Mi smj2386)  

This article is cited in 17 scientific papers (total in 17 papers)

Stationary solutions to the equations of dynamics of mixtures of heat-conductive compressible viscous fluids

N. A. Kuchera, A. E. Mamontovb, D. A. Prokudina

a Kemerovo State University, Kemerovo, Russia
b Lavrent'ev Institute of Hydrodynamics, Novosibirsk, Russia
References:
Abstract: We consider the equations describing the three-dimensional steady motions of binary mixtures of heat-conductive compressible viscous fluids. An existence theorem for the boundary value problem that corresponds to flows in a bounded domain is proved in the class of weak generalized solutions.
Keywords: boundary value problem, dynamics of mixtures, Navier–Stokes equations, weak solutions.
Received: 30.09.2011
Revised: 21.06.2012
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 6, Pages 1075–1088
DOI: https://doi.org/10.1134/S0037446612060110
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: N. A. Kucher, A. E. Mamontov, D. A. Prokudin, “Stationary solutions to the equations of dynamics of mixtures of heat-conductive compressible viscous fluids”, Sibirsk. Mat. Zh., 53:6 (2012), 1338–1353; Siberian Math. J., 53:6 (2012), 1075–1088
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/smj2386
  • https://www.mathnet.ru/eng/smj/v53/i6/p1338
  • This publication is cited in the following 17 articles:
    1. D. A. Zakora, “Zadacha o malykh dvizheniyakh smesi vyazkikh szhimaemykh zhidkostei”, Sib. elektron. matem. izv., 20:2 (2023), 1552–1589  mathnet  crossref
    2. A. E. Mamontov, D. A. Prokudin, “Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids”, J. Appl. Industr. Math., 15:1 (2021), 50–61  mathnet  crossref  crossref  elib
    3. N. A. Kucher, A. A. Zhalnina, O. V. Malyshenko, “O suschestvovanii silnykh reshenii regulyarizovannykh uravnenii smesi vyazkikh szhimaemykh zhidkostei”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 64, 31–47  mathnet  crossref
    4. A E Mamontov, D A Prokudin, “Global unique solvability of the initial-boundary value problem for one-dimensional barotropic equations of viscous compressible bifluids”, J. Phys.: Conf. Ser., 1666:1 (2020), 012032  crossref
    5. Piasecki T., Shibata Y., Zatorska E., “on Strong Dynamics of Compressible Two-Component Mixture Flow”, SIAM J. Math. Anal., 51:4 (2019), 2793–2849  crossref  mathscinet  zmath  isi
    6. A. E. Mamontov, D. A. Prokudin, “Viscous compressible homogeneous multi-fluids with multiple velocities: barotropic existence theory”, Sib. elektron. matem. izv., 14 (2017), 388–397  mathnet  crossref
    7. D. A. Prokudin, “Ob odnoznachnoi razreshimosti nachalno–kraevoi zadachi dlya modelnoi sistemy uravnenii politropnogo dvizheniya smesi vyazkikh szhimaemykh zhidkostei”, Sib. elektron. matem. izv., 14 (2017), 568–585  mathnet  crossref
    8. N. A. Kucher, A. A. Zhalnina, “On the existence of global solutions to equations for mixtures of compressible viscous fluids”, All-Russian Conference With International Participation on 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. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012048  crossref  isi  scopus
    9. A. Mamontov, D. Prokudin, “Global solvability of 1D equations of viscous compressible multi-fluids”, All-Russian Conference With International Participation on 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. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012059  crossref  isi  scopus
    10. A. Mamontov, D. Prokudin, “Modeling viscous compressible barotropic multi-fluid flows”, All-Russian Conference With International Participation on 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. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012058  crossref  isi  scopus
    11. A. A. Papin, M. A. Tokareva, “Correctness of the initial-boundary problem of the compressible fluid filtration in a viscous porous medium”, All-Russian Conference With International Participation on 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. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012070  crossref  isi  scopus
    12. A. E. Mamontov, D. A. Prokudin, “Local solvability of the initial-boundary value problem for one-dimensional equations of polytropic flows of viscous compressible multifluids”, J. Math. Sci., 231:2 (2018), 227–242  mathnet  crossref  crossref
    13. D. A. Prokudin, M. V. Krayushkina, “Solvability of a steady boundary value problem for a model system of equations of a barotropic motion of a mixture of viscous compressible fluids”, J. Appl. Industr. Math., 10:3 (2016), 417–428  mathnet  crossref  crossref  mathscinet  elib
    14. A. E. Mamontov, D. A. Prokudin, “Razreshimost statsionarnoi kraevoi zadachi dlya uravnenii politropnogo dvizheniya vyazkikh szhimaemykh mnogozhidkostnykh sred”, Sib. elektron. matem. izv., 13 (2016), 664–693  mathnet
    15. A. E. Mamontov, D. A. Prokudin, “Solvability of the regularized steady problem of the spatial motions of multicomponent viscous compressible fluids”, Siberian Math. J., 57:6 (2016), 1044–1054  mathnet  crossref  crossref  isi  elib
    16. Mucha P.B., Pokorny M., Zatorska E., “Heat-Conducting, Compressible Mixtures With Multicomponent Diffusion: Construction of a Weak Solution”, SIAM J. Math. Anal., 47:5 (2015), 3747–3797  crossref  mathscinet  zmath  isi  elib  scopus
    17. A. E. Mamontov, D. A. Prokudin, “Solubility of a stationary boundary-value problem for the equations of motion of a one-temperature mixture of viscous compressible heat-conducting fluids”, Izv. Math., 78:3 (2014), 554–579  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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