We study the existence of global continuous sonic–supersonic flows in a two-dimensional semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is sonic at the inlet of the duct. One of the main difficulties for the global existence is that the 2D steady Euler system becomes degenerate at the inlet of the duct. To overcome this difficulty, we establish some uniform interior \(C^{0, 1}\) estimates for the global supersonic solutions to a sequence of regularized problems, and then use the Arzela–Ascoli theorem and a standard diagonal procedure to construct a global continuous sonic–supersonic solution in the duct. Sufficient conditions for the existence or nonexistence of vacuum in the duct are also given.

我们研究了二维半无限发散管道中全球连续音速-超音速流动的存在。流动满足管道壁上的滑移条件，并且在管道入口处的流动状态为声波。全局存在的主要困难之一是二维稳态欧拉系​​统在管道入口处退化。为了克服这个困难，我们为一系列正则化问题的全局超音速解建立了一些统一的内部\(C^{0, 1}\)估计，然后使用 Arzela-Ascoli 定理和标准对角线程序来构建一个管道中的全局连续声-超音速解。还给出了管道中真空存在或不存在的充分条件。