Incompressible impinging jet flow with gravity

In this paper, we investigate steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle, falling under gravity impinging onto horizontal wall. More precisely, for any given atmosphere pressure $$p_{atm}$$ appropriate incoming total flux Q, establish the existence jet with gravity. The two free surfaces initiate smoothly at endpoints nozzle become to be in downstream. By transforming boundary problem into minimum problem, properties flow region boundaries. Moreover, asymptotic behavior upstream downstream is also obtained.