Supersonic Flow Over Slope Weak Shock Wave Solution Of The Local Existence And Uniqueness

In this paper, we study the local existence and uniqueness of weak shocks in steady supersonic flow past a wedge. We take the potential flow equation as the mathematical model to describe the compressible flow. It is known that in generic case such a problem admits two possible locations of the shock front, connecting the flow ahead of it and behind it, provided that the vertex angle of the wedge is less than a critical value. They can be distinguished as supersonic-supersonic shock and supersonic-subsonic shock(or transonic shock). Both these possible shocks satisfy the Rankine-Hugoniot conditions and entropy condition. In this paper we prove the local existence and uniqueness of weak shock front if the coming flow is under small disturbance.