Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system (Q2250577)

The authors consider the Cauchy problem for the isentropic Euler system in two spatial dimensions. The initial data are smooth at both sides of a smooth curve, but are discontinuous on this curve. Local existence of a piecewise smooth solution is proven. The solution contains three kids of singularities: shock wave, rarefaction wave, and contact discontinuity. The proof is based on an accompanying one-dimensional Riemann problem.