Abstract:
In this paper we study the mathematical aspects of the stationary supersonic flow past a non-axisymmetric curved pointed body. The flow is described by a steady potential flow equation, which is a quasilinear hyperbolic equation of second order. We prove the local existence of the solution to this problem with a pointed shock attached at the tip of the pointed body, provided the pointed body is a perturbation of a circular cone, and the vertex angle of the approximate cone of the pointed body is less than a critical value. The solution is smooth in between the shock and the surface of the body. Consequently, such a structure of flow near the tip of the pointed body and its stability is verified mathematically.
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Accepted October 13, 2000¶Published online January 22, 2001
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Chen, S. Existence of Stationary Supersonic Flows Past a Pointed Body. Arch. Rational Mech. Anal. 156, 141–181 (2001). https://doi.org/10.1007/s002050100121
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DOI: https://doi.org/10.1007/s002050100121