The Structure Of The Solutions Of Two-dimensional Simplified Euler Equations

We investigate the structure of the solution of the two dimensional Riemann problem of the simplified Euler system with smooth initial discontinuity curve. when the initial condition and the initial discontinuity are related in certain ways, the solutions have been investigated. We discuss some cases where they assume different relations over different regions of the plane.The stability of rarefaction solution relative to perturbations of the initial discontinuity is also investigated.