# SMOOTH TRANSONIC FLOWS AROUND CONES

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

## 摘要

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.

原文 English 827-845 19 Networks and Heterogeneous Media 17 6 https://doi.org/10.3934/nhm.2022028 Published - 2022 12月

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