We consider questions of well-posedness and existence of solutions near pipe fittings for models based on the nonlinear hyperbolic partial differential equations which are derived from the Euler equations. The problem at hand is an initial and boundary value problem for a system of nonlinear conservation laws coupled by the conditions introduced by the pipe fitting.
The applied techniques are based on considerations on special Riemann problems posed at the pipe fitting. Finally, we present numerical examples showing the dynamics on the pipe and at the pipe fitting.