  In the classical survey (Chapter 16.2, {\it Mathematics in industrial
problem}, Vol. 24, Springer-Verlag, New York, 1989), A. Friedman proposed an
open problem on the collision of two incompressible jets emerging from two
axially symmetric nozzles. In this paper, we concerned with the mathematical
theory on this collision problem, and establish the well-posedness theory on
hydrodynamic impinging outgoing jets issuing from two coaxial axially symmetric
nozzles. More precisely, we showed that for any given mass fluxes $M_1>0$ and
$M_2<0$ in two nozzles respectively, that there exists an incompressible,
inviscid impinging outgoing jet with contact discontinuity, which issues from
two given semi-infinitely long axially symmetric nozzles and extends to
infinity. Moreover, the constant pressure free stream surfaces of the impinging
jet initiate smoothly from the mouths of the two nozzles and shrink to some
asymptotic conical surface. There exists a smooth surface separating the two
incompressible fluids and the contact discontinuity occurs on the surface.
Furthermore, we showed that there is no stagnation point in the flow field and
its closure, except one point on the symmetric axis. Some asymptotic behavior
of the impinging jet in upstream and downstream, geometric properties of the
free stream surfaces are also obtained. The main results in this paper solved
the open problem on the collision of two incompressible axially symmetric jets
in [24].
