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The convexity of compressible subsonic impinging jet flows

We proved the existence and uniqueness of compressible subsonic impinging jet flow in previous work. As a continuation, in this paper, we investigate the shape of free boundary to the impinging jet flow. More specifically, if the nozzle wall is concave to the fluid, then the free boundary of flow will be convex to the fluid. On another hand, the higher regularity of free boundary at separation point is obtained, provided that the nozzle satisfies corresponding hypotheses.