Archive for Rational Mechanics and Analysis

, Volume 156, Issue 2, pp 141–181

Existence of Stationary Supersonic Flows Past a Pointed Body

  • Shuxing Chen

DOI: 10.1007/s002050100121

Cite this article as:
Chen, S. Arch. Rational Mech. Anal. (2001) 156: 141. doi:10.1007/s002050100121


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Shuxing Chen
    • 1
  1. 1.Institute of Mathematics¶Fudan University¶Shanghai, 200433¶China¶E-mail: sxchen¶