This paper concerns subsonic-sonic potential flows in general two dimensional nozzles. For finitely long symmetric nozzles, we formulate the subsonic-sonic flow problem by prescribing the flow angle at the inlet and the outlet. It is shown that this problem admits a unique Lipschitz continuous subsonic-sonic flow, and the sonic points of the flow must occur at the wall or the throat. This is the first result on the well-posedness for general subsonic-sonic flow problems. More importantly, the location of sonic points is classified completely. Indeed, it is shown that there exists a critical value depending only on the length and the geometry of the nozzle such that the flow is sonic on the whole throat if the height of the nozzle is not greater than this critical value, while the sonic points must be located at the wall if the height is greater than this value. Furthermore, the critical height is positive iff the nozzle is suitably flat near the throat. As a direct application of this theory, we can obtain conditions on whether there is a smooth transonic flow of Meyer type whose sonic points are all exceptional in de Laval nozzles.

本文涉及一般二维喷嘴中的亚音速声势流。对于有限长的对称喷嘴，我们通过规定入口和出口的流动角度来制定亚音速流问题。结果表明，该问题允许出现唯一的Lipschitz连续亚音速流，并且该流的声波点必须出现在壁或咽喉处。这是一般亚音速流问题的适定性的第一个结果。更重要的是，对声波点的位置进行了完全分类。实际上，已显示存在一个仅取决于喷嘴的长度和几何形状的临界值，因此，如果喷嘴的高度不大于该临界值，则整个喉咙上的声音都是声波，如果声波点的高度大于此值，则声波点必须位于墙壁上。此外，如果喷嘴在喉部附近适当平坦，则临界高度为正。作为该理论的直接应用，我们可以得出关于是否存在光滑的Meyer型跨音速流的条件，该音速在de Laval喷嘴中都是异常的。