Wen Ching Lien, Yu-Yu Liu, Chen Chang Peng

Research output: Contribution to journalArticlepeer-review


We consider a conical body facing a supersonic stream of air at a uniform velocity. When the opening angle of the obstacle cone is small, the conical shock wave is attached to the vertex. Under the assumption of self-similarity for irrotational motions, the Euler system is transformed into the nonlinear ODE system. We reformulate the problem in a non-dimensional form and analyze the corresponding ODE system. The initial data is given on the obstacle cone and the solution is integrated until the Rankine-Hugoniot condition is satisfied on the shock cone. By applying the fundamental theory of ODE systems and technical estimates, we construct supersonic solutions and also show that no matter how small the opening angle is, a smooth transonic solution always exists as long as the speed of the incoming flow is suitably chosen for this given angle.

Original languageEnglish
Pages (from-to)827-845
Number of pages19
JournalNetworks and Heterogeneous Media
Issue number6
Publication statusPublished - 2022 Dec

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics


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