Conjecture on the Structure of Solutions of the Riemann Problem for Two-Dimensional Gas Dynamics Systems

Abstract

Two-dimensional flow of polytropic gas with initial data being constant in each quadrant is considered. Under the assumption that each jump in initial data outside of the origin projects exactly one planar wave of shocks, centered rarefaction waves, or slip planes, it is proved that only 16 combinations of initial data are reasonable. For each combination, a conjecture on the structure of the solution in the whole space $t > 0$ is given.