January & February  2009, 23(1&2): 115-132. doi: 10.3934/dcds.2009.23.115

Weak shock solution in supersonic flow past a wedge

1. 

School of Mathematical Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China

Received  November 2007 Revised  April 2008 Published  September 2008

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 that 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.
Citation: Shuxing Chen, Jianzhong Min, Yongqian Zhang. Weak shock solution in supersonic flow past a wedge. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 115-132. doi: 10.3934/dcds.2009.23.115
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