xistence condition of one-dimensional self-similar motion of ideal gas

The extension criterion of ideal gas self-similarity motion is not verycomplete. Hydrodynamic equations are made dimensionless, and then we obtainthe basic characteristic quantities solutions of ideal gas one-dimensionalself-similarity differential equations described by relative coordinate \xi and distance r. All of them have the same form Y ( \xi ,r ) =y ( \xi ) r^C_Y , which means that characteristic quantities forevery certain \xi are spatial scale-invariant according to r. It is provedthat the spatial scale-invariant is the existence condition ofone-dimensional ideal gas self-similarity motion.