INCOMPRESSIBLE JET FLOW PAST AN OBSTACLE

This paper is concerned with the well-posedness of the incompressible jet flow issuing from a semi-infinitely long nozzle and moving around an obstacle. More precisely, we prove that one can find a differential pressure, such that there exists a unique solution to the incompressible jet flow, with the upper free boundary initiating smoothly from the endpoint of the nozzle wall and the lower free boundary initiating smoothly from the surface of the obstacle. Moreover, the nonexistence of a finite cavity between the cavity boundary and the obstacle is established. On another side, we obtain the optimal regularity at the detachment of the lower free boundary.