Geodesic
Application of Megrabov's differential identities to the two-velocity hydrodynamics equations with one pressure
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 156-163 Cet article a éte moissonné depuis la source Math-Net.Ru

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A series of the differential identities connecting velocities, pressure and body force in the two-velocity hydrodynamics equations with equilibrium of pressure phases are found. Some of these identities have a divergent form and can be considered as some conservation laws. It is detected that the flow functions for plane motion satisfy the Monge–Ampere system of equations.
Keywords: two-velocity hydrodynamics, hyperbolic system. 
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     title = {Application of {Megrabov's} differential identities to the two-velocity hydrodynamics equations with one pressure},
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Nasriddin M. Zhabborov; Petr V. Korobov; Kholmatzhon Kh. Imomnazarov. Application of Megrabov's differential identities to the two-velocity hydrodynamics equations with one pressure. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 156-163. http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a1/

[1] V. M. Neschadim, “Obratnye zadachi dlya kineticheskikh uravnenii. Algebraicheskie i differentsialnye tozhdestva”, Dokl. RAN, 400:3 (2005), 315–318 | MR

[2] A. G. Megrabov, “Differentsialnye tozhdestva, svyazyvayuschie laplasian skalyarnoi funktsii, modul ee gradienta i ugol ego napravleniya”, Dokl. RAN, 424:5 (2009), 599–603 | MR | Zbl

[3] A. G. Megrabov, “Differentsialnye tozhdestva, svyazyvayuschie modul i napravleniya vektornogo polya, gidrodinamicheskie uravneniya Eilera”, Dokl. RAN, 433:3 (2010), 309–313 | MR | Zbl

[4] N. E. Kochin, Vektornoe ischislenie i nachala tenzornogo ischisleniya, GONTI, L.–M., 1938

[5] V. N. Dorovskii, “Kontinualnaya teoriya filtratsii”, Geologiya i geofizika, 1989, no. 7, 39–45

[6] V. N. Dorovskii, Yu. V. Perepechko, “Fenomenologicheskoe opisanie dvukhskorostnykh sred s relaksiruyuschimi kasatelnymi napryazheniyami”, PMTF, 1992, no. 3, 94–105

[7] V. N. Dorovskii, Yu. V. Perepechko, “Teoriya chastichnogo plavleniya”, Geologiya i geofizika, 1989, no. 9, 56–64