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SOME ELEMENTARY INEQUALITIES IN GAS DYNAMICS EQUATION

**SOME** **ELEMENTARY** **IN**EQUALITIES**IN** **GAS** **DYNAMICS** **EQUATION** V. A. KLYACH**IN**, A. V. KOCHETOV, AND V. M. MIKLYUKOV Received 12 January 2005; Accepted 25 August 2005 We describe the sets on which difference of solutions of the gas dynamics equation satisfy some special conditions. By virtue of nonlinearity of the equation the sets depend on the solution gradient quantity. We show double-ended estimates of the given sets and some properties of these estimates. Copyright © 2006 V. A. Klyachin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Main results Consider the gas dynamics equation where n ∂ σ |∇ f | fxi = 0, (1.1) ∂xi c=1 γ − 1 σ(t) = 1 − 2 t2 1/(γ−1) . (1.2) Here γ is a constant, −∞

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