The main purpose of this paper is to show the well-posedness theory of two-dimensional symmetric compressible subsonic impinging jet flow. More precisely, for any given atmospheric pressure, we show that there exists a critical value, such that if the incoming mass flux is less than the critical value, then there exists a smooth symmetric compressible subsonic impinging jet flow, and the free boundary of the flow detaches smoothly from the end points of the nozzle. Moreover, the asymptotic behavior at the far field and the positivity of horizontal velocity of the flow are also obtained. On the other hand, under the star-shaped condition on the given nozzle, we will get the uniqueness of compressible subsonic impinging jet flow. Finally, we show that the vertical velocity of the flow is positive under the monotonous hypothesis on the upper nozzle wall.

中文翻译：

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任意喷嘴中可压缩亚音速撞击射流的存在

本文的主要目的是展示二维对称可压缩亚音速撞击射流的适定性理论。更准确地说，对于任何给定的大气压力，我们证明存在一个临界值，这样如果进入的质量通量小于临界值，则存在平滑对称的可压缩亚音速撞击射流，并且流从喷嘴的端点顺利分离。此外，还获得了远场的渐近行为和流动的水平速度的正性。另一方面，在给定喷嘴上的星形条件下，我们将得到可压缩亚音速撞击射流的唯一性。最后，