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

Weak shock solution in supersonic flow past a wedge


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 weakshock solution in steady supersonic flow past a wedge. We take the 3-D potential flow equation as the mathematical model todescribe the compressible flow. It is known that when a supersonicflow passes a wedge, there will appear an attached shock front,provided that the vertex angle of the wedge is less than a criticalvalue. In generic case the problem admits two possible locations ofthe shock front, connecting the flow ahead of it and behind it. They can bedistinguished as supersonic-supersonic shock and supersonic-subsonicshock (or transonic shock). In this paper we prove the localexistence and uniqueness of weak shock front if the coming flow is asmall perturbation of a constant supersonic flow. Our analysis isbased on the usage of partial hodograph transformation and domaindecomposition, which let the proof be simpler than the previousdiscussion.
Citation: Shuxing Chen, Jianzhong Min, Yongqian Zhang. Weak shock solution in supersonic flow past a wedge. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 115-132. doi: 10.3934/dcds.2009.23.115

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