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”, Sib. Zh. Ind. Mat., 19:3 (2016), 55–67; J. Appl. Industr. Math., 10:3 (2016), 417

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Sibirskii Zhurnal Industrial'noi Matematiki, 2016, Volume 19, Number 3, Pages 55–67
DOI: https://doi.org/10.17377/sibjim.2016.19.305 (Mi sjim928)

This article is cited in 16 scientific papers (total in 16 papers)

Solvability of a steady boundary value problem for a model system of equations of a barotropic motion of a mixture of viscous compressible fluids

D. A. Prokudin^a, M. V. Krayushkina^b

^a Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk
^b Kemerovo State University, 6 Krasnaya str., 650043 Kemerovo

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DOI: https://doi.org/10.17377/sibjim.2016.19.305

Abstract: We consider a boundary value problem for a model system of equations describing a steady barotropic motion of a homogeneous mixture of viscous compressible fluids in a bounded three-dimensional domain. An existence theorem is proved for weak solutions to the problem without constraints on the structure of the total viscosity matrix except the standard requirements of positive definiteness.

Keywords: existence theorem, steady boundary value problem, viscous compressible fluid, homogeneous mixture with two velocities, effective viscous flux.

Funding agency	Grant number
Russian Science Foundation	15-11-20019

Received: 20.07.2015

English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 3, Pages 417–428
DOI: https://doi.org/10.1134/S1990478916030121

Bibliographic databases:

Document Type: Article

UDC: 517.95

Language: Russian

Citation: 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”, Sib. Zh. Ind. Mat., 19:3 (2016), 55–67; J. Appl. Industr. Math., 10:3 (2016), 417–428

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Linking options:

https://www.mathnet.ru/eng/sjim928

https://www.mathnet.ru/eng/sjim/v19/i3/p55

This publication is cited in the following 16 articles:

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
D. A. Prokudin, “Existence of weak solutions to the problem on three-dimensional steady heat-conductive motions of compressible viscous multicomponent mixtures”, Siberian Math. J., 62:5 (2021), 895–907
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
A. E. Mamontov, D. A. Prokudin, “Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluids”, J. Math. Fluid Mech., 21:1 (2019), UNSP 9
A. E. Mamontov, D. A. Prokudin, “Global Estimates and Solvability of the Regularized Problem About Three-Dimensional Non-Stationary Motion of Viscous Compressible Heat-Conducting Multi-Component Liquid”, Sib. Electron. Math. Rep., 16 (2019), 547–590
Alexander Mamontov, Dmitry Prokudin, “Global solvability of the initial-boundary value problem for Navier–Stokes–Fourier type equations describing flows of viscous compressible heat-conducting multifluids”, J. Phys.: Conf. Ser., 1268:1 (2019), 012061
A. E. Mamontov, D. A. Prokudin, “Solubility of unsteady equations of multi-component viscous compressible fluids”, Izv. Math., 82:1 (2018), 140–185
A. E. Mamontov, D. A. Prokudin, “Unique solvability of initial-boundary value problem for one-dimensional equations of polytropic flows of multicomponent viscous compressible fluids”, Sib. Electron. Math. Rep., 15 (2018), 631–649
A. Mamontov, D. Prokudin, “Global solvability of 1D equations of viscous compressible multi-fluids”, 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. 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 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 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, “Viscous Compressible Homogeneous Multi-Fluids With Multiple Velocities: Barotropic Existence Theory”, Sib. Electron. Math. Rep., 14 (2017), 388–397
D. A. Prokudin, “Unique Solvability of Initial-Boundary Value Problem For a Model System of Equations For the Polytropic Motion of a Mixture of Viscous Compressible Fluids”, Sib. Electron. Math. Rep., 14 (2017), 568–585
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
A. E. Mamontov, D. A. Prokudin, “Solubility of steady boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids”, Sib. Electron. Math. Rep., 13 (2016), 664–693
A. E. Mamontov, D. A. Prokudin, “Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids”, Sib. Electron. Math. Rep., 13 (2016), 541–583

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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