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.
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
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\paper Stationary solutions to the equations of dynamics of mixtures of heat-conductive compressible viscous fluids
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\pages 1338--1353
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 6
\pages 1075--1088
\crossref{https://doi.org/10.1134/S0037446612060110}
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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:
D. A. Zakora, “Zadacha o malykh dvizheniyakh smesi vyazkikh szhimaemykh zhidkostei”, Sib. elektron. matem. izv., 20:2 (2023), 1552–1589
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
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
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
Piasecki T., Shibata Y., Zatorska E., “on Strong Dynamics of Compressible Two-Component Mixture Flow”, SIAM J. Math. Anal., 51:4 (2019), 2793–2849
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
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
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
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
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
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
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
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
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
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
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