有限长管道中具有重力的冲击喷流的适定性

Wellposedness of the impinging jet flow with gravity in a finitely long nozzle

具有重力的冲击喷流问题在工程环境和自然界中非常常见,如喷泉和瀑布等.本文研究具有重力的定常不可压缩理想流体动力学中的冲击喷流问题,建立有限长管道中具有重力的冲击喷流的数学理论.本文证明对于给定有限长管道入口来流的初始速度和大气压力,存在光滑的冲击喷流使得自由边界光滑地连接到管道的尾点.进一步地,本文研究管道入口角点附近解的正则性、冲击喷流在下游的渐近行为以及参数的唯一性.

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 fow problem in the steady incompressible ideal fuid 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 fow 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.