Nasriddin M. Zhabborov, Petr V. Korobov, Kholmatzhon Kh. Imomnazarov, “Application of Megrabov's differential identities to the two-velocity hydrodynamics equations with one pressure”, J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 2,Pages <nobr>156

Application of Megrabov's differential identities to the two-velocity hydrodynamics equations with one pressure

Nasriddin M. Zhabborov^a, Petr V. Korobov^b, Kholmatzhon Kh. Imomnazarov^b

^a National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan
^b Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: 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.

UDC: 517.9

Received: 29.11.2011
Received in revised form: 29.12.2011
Accepted: 10.01.2012