Classification of the Riemann Problem for Two-Dimensional Gas Dynamics

The Riemann problem for two-dimensional gas dynamics with isentropic and polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave or slip line connects two neighboring constant initial states. With this restriction, the existence of sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas is proved. For each configuration the relations for the initial data and the symmetry properties of the solution are given. This paper corrects the, conjectured classification presented in T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630].