On one two-dimensional stationary flow of a binary mixture and viscous fluid in a plane layer
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 30-36.

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Nonlinear model of convection in Oberbeck–Boussinesq approximation describing the flat joint motion of a binary mixture and viscous fluid with a common interface is investigated. It is important that the longitudinal temperature gradient and the concentration is quadratic dependence on the coordinate $x$. Stationary solution of the system is built.
Keywords: Oberbeck-Boussinesq equations, convective motion, binary mixture, steady flow.
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Marina V. Efimova. On one two-dimensional stationary flow of a binary mixture and viscous fluid in a plane layer. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 30-36. http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a3/

[1] G. A. Ostroumov, Free convection under the conditions of the internal problem, National Advisory Committee for Aeronautics, Washington, 1958

[2] R. V. Birikh, “Thermocapillary convection in a horizontal layer of liquid”, J. Appl. Mech. Tech. Phys., 5 (1966), 69–72

[3] V. K. Andreev, Birikh solution of convection equations and some their generalizations, Preprint of ICM SB RAS, Krasnoyarsk, 2010 (in Russian) | MR

[4] V. K. Andreev, I. V. Stepanova, “Ostroumov–Birikh solution of convection equations with nonlinear buoyancy force”, Applied Mathematics and Computation, 228 (2014), 59–67 | DOI | MR

[5] V. V. Pukhnachov, “Group-theoretical nature of the Birikh solution and its generalizations”, Symmetries and Differential Equation, Trudy rossiiskoi konferentsii po simmetrii i differentsial'nym uravneniyam, Inst. Comput. Modeling, Sib. Branch Russian Acad. of Sci., Krasnoyarsk, 2000, 180–183 (in Russian)

[6] O. N. Goncharova, O. A. Kabov, V. V. Pukhnachov, “Solutions of special type describing the three dimensional thermocapillary flows with an interface”, Int. J. Heat Mass Transfer, 55:4 (2012), 715–725 | DOI | Zbl

[7] V. V. Pukhnachov, “Non-stationary Analogues of the Birikh Solution”, Nauchnyi zhurnal teoreticheskih i prikladnyh issledovanii. Novosti Altaiskogo Gos. Universiteta, 69:1–2 (2011), 62–69 (in Russian)