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Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations

A. A. Zlotnik<sup>ab

a</sup> Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya ul. 14, Moskow, 111250 Russia
^b Department of Applied Mathematics, Russian State Social University, ul. W. Pieck 4, Moskow, 129226 Russia

Abstract: Energy equalities are derived for the barotropic quasi-gasdynamic, modified quasi-gasdynamic, and quasi-hydrodynamic systems of equations. Global energy estimates of solutions are obtained. For the second of the systems, necessary and sufficient conditions for nonuniform and uniform Petrovskii parabolicity are derived.

Key words: gas dynamics, quasi-gasdynamic system of equations, energy equality, Petrovskii parabolicity.

UDC: 519.634

Received: 27.07.2009
Revised: 14.08.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:2, 310–321

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