Transonic Shock Formation in a Rarefaction Riemann Problem for the 2D Compressible Euler Equations

It is perhaps surprising for a shock wave to exist in the solution of a rarefaction Riemann problem for the compressible Euler equations in two space dimensions. We present numerical evidence and generalized characteristic analysis to establish the existence of a shock wave in such a 2D Riemann problem, defined by the interaction of four rarefaction waves. We consider both the customary configuration of waves at the right angle and also an oblique configuration for the rarefaction waves. Two distinct mechanisms for the formation of a shock wave are discovered as the angle between the waves is varied. AMS subject classification (2000). Primary: 35L65, 35J70, 35R35; Secondary: 35J65.