Simple waves of the two dimensional compressible full euler equations

In this paper, we establish the existence of four families of simple wave solution for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4 × 4 non-reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0=λ1,λ2,λ3 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.