On some identities in gas dynamics

Three identities that govern the macroparameters of an ideal polytropic gas are proven. With their help the equivalence of two different forms of writing the non-stationary Euler system on class of continuously differentiable functions is established. It is shown that any infinitely differentiable solution of a stationary Euler system under some additional conditions is also a solution of stationary Navier-Stokes system and stationary quasi-gas-dynamic system.