Abstract The transonic channel flow problem is one of the most important problems in mathematical fluid dynamics. The structure of solutions near the sonic curve is a key part of the whole transonic flow problem. This paper constructs a local classical hyperbolic solution for the 3-D axisymmetric steady compressible full Euler equations with boundary data given on the degenerate hyperbolic curve. By introducing a novel set of dependent and independent variables, we use the idea of characteristic decomposition to transform the axisymmetric Euler equations as a new system which has explicitly singularity-regularity structures. We first establish a local classical solution for the new system in a weighted metric space and then convert the solution in terms of the original variables.

中文翻译：

---

关于轴对称的 3-D 稳态全欧拉方程的退化双曲线问题

摘要 跨音速通道流动问题是数学流体动力学中最重要的问题之一。声速曲线附近解的结构是整个跨音速流动问题的关键部分。本文为 3-D 轴对称稳态可压缩全欧拉方程构造了局部经典双曲线解，边界数据在退化双曲线上给出。通过引入一组新的因变量和自变量，我们使用特征分解的思想将轴对称欧拉方程转换为具有明确奇点-正则结构的新系统。我们首先在加权度量空间中为新系统建立局部经典解，然后根据原始变量转换解。