Geodesic
Stationary solutions of a boundary value problem for equations of barotropic flow of multicomponent media
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 959-971.

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The problem of steady barotropic motion of a multicomponent medium consisting of viscous compressible fluids in a bounded domain of three-dimensional space is formulated. The solvability of the problem is proved. Viscosity matrices are assumed to be arbitrary (non-diagonal).
Keywords: existence theorem, steady barotropic flow, viscosity matrix.
Mots-clés : viscous compressible multifluid 
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A. E. Mamontov; D. A. Prokudin. Stationary solutions of a boundary value problem for equations of barotropic flow of multicomponent media. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 959-971. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a40/

[1] A.M. Blokhin, V.N. Dorovskii, Problems of mathematical modeling in the theory of a multivelocity continuum, Nauka, Novosibirsk, 1994 | MR

[2] R. Coifman, Y. Meyer, “On commutators of singular integrals and bilinear singular integrals”, Trans. Am. Math. Soc., 212 (1975), 315–331 | DOI | MR | Zbl

[3] V.N. Dorovskii, Yu.V. Perepechko, “Phenomenological description of two-velocity media with relaxing shear stresses”, J. Appl. Mech. Tech. Phys., 33:3 (1992), 403–409 | DOI

[4] E. Feireisl, A. Novotný, Singular limits in thermodynamics of viscous fluids, Advances in Mathematical Fluid Mechanics, Birkhäuser, Basel, 2009 | MR | Zbl

[5] J. Frehse, S. Goj, J. Málek, “On a Stokes-like system for mixtures of fluids”, SIAM J. Math. Anal., 36:4 (2005), 1259–1281 | DOI | MR | Zbl

[6] J. Frehse, W. Weigant, “On quasi-stationary models of mixtures of compressible fluids”, Appl. Math., Praha, 53:4 (2008), 319–345 | DOI | MR | Zbl

[7] P.-L. Lions, Mathematical topics in fluid mechanics, v. 2, Compressible models, Clarendon Press, Oxford, 1998 | MR | Zbl

[8] A.E. Mamontov, D.A. Prokudin, “Viscous compressible multi-fluids: modeling and multi-D existence”, Methods Appl. Anal., 20:2 (2013), 179–196 | DOI | MR | Zbl

[9] A.E. Mamontov, D.A. Prokudin, “Solubility of steady boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids”, Sib. Èlectron. Mat. Izv., 13 (2016), 664–693 | MR | Zbl

[10] A.E. Mamontov, D.A. Prokudin, “Solvability of the regularized steady problem of the spatial motions of multicomponent viscous compressible fluids”, Sib. Math. J., 57:6 (2016), 1044–1054 | DOI | MR | Zbl

[11] R.I. Nigmatulin, Dynamics of multiphase media, v. 1, Hemisphere, New York, 1990

[12] A. Novotný, I. Straškraba, Introduction to the mathematical theory of compressible flow, Oxford Lecture Series in Mathematics and Its Applications, 27, Oxford University Press, Oxford, 2004 | MR

[13] K.L. Rajagopal, L. Tao, Mechanics of mixtures, Series on Advances in Mathematics for Applied Sciences, 35, World Scientific, Singapore, 1995 | MR | Zbl

[14] L. Tartar, “Compensated compactness and applications to partial differential equations”, Nonlinear analysis and mechanics, Heriot-Watt Symp. (Edinburgh 1979), v. 4, Res. Notes Math., 39, Pitman, Boston etc., 1979, 136–212 | MR | Zbl