The impinging jet flows with gravity are very common in engineering environments and nature,such as fountains and waterfalls.In this paper,we study the impinging jet flow problem in the steady incompressible ideal fluid dynamics with gravity and establish the mathematical theory of impinging jet flows with gravity in a finitely long nozzle.We prove that for any given initial velocity field in the inlet of the nozzle and atmospheric pressure value,there exists a smooth impinging jet flow with the free boundary initiated smoothly at the endpoints of the nozzle.Moreover,we investigate the regularity of the solution near the corner point in the inlet of the nozzle,the asymptotic behavior of the impinging jet flow in the downstream,and the uniqueness of the parameter.
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