WEAK SHOCK SOLUTION IN SUPERSONIC FLOW PAST A WEDGE

In this paper we study the local existence and uniqueness of weak shock solution in steady supersonic flow past a wedge. We take the 3-D potential flow equation as the mathematical model to describe the compressible flow. It is known that when a supersonic flow passes a wedge, there will appear an attached shock front, provided the vertex angle of the wedge is less than a critical value. In generic case the problem admits two possible locations of the shock front, connecting the flow ahead of it and behind it. They can be distinguished as supersonic-supersonic shock and supersonic-subsonic shock (or transonic shock). In this paper we prove the local existence and uniqueness of weak shock front if the coming flow is a small perturbation of a constant supersonic flow. Our analysis is based on the usage of partial hodograph transformation and domain decomposition, which let the proof be simpler than the previous discussion.