This paper establishes the existence and uniqueness of continuous/smooth Meyer type transonic solutions to the quasi-one-dimensional steady isentropic relativistic Euler equations. We use the high-order Taylor’s expansion of the velocity near the sonic point to overcome the difficulties of applying the implicit function theorem caused by the sonic degeneracy. It is verified that the flow in the De Laval nozzle accelerates from subsonic upstream and continuously/smoothly pass through the sonic surface at the throat and then becomes supersonic downstream. Moreover, the flow may have a zero or positive acceleration at the sonic surface, which depends on the geometric property of the nozzle at the throat.

中文翻译：

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准一维稳态相对论欧拉方程的连续/平滑跨音速解


本文建立了准一维稳态等熵相对论性欧拉方程的连续/光滑Meyer型跨音速解的存在性和唯一性。我们利用声速点附近速度的高阶泰勒展开来克服声速简并性带来的应用隐函数定理的困难。经验证，德拉瓦尔喷管内的流动从上游亚音速开始加速，连续/平滑地穿过喉部的声速表面，然后在下游变成超音速。此外，流动在声速表面处可能具有零或正加速度，这取决于喉部处喷嘴的几何特性。