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Weak shock solution in supersonic flow past a wedge

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  • 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.
    Mathematics Subject Classification: Primary: 35L70, 35L65,35L67; Secondary: 76N15.


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