The steady state collision of two compressible subsonic perfect flows

This paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles. We established the existence, uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady Euler system in an important physical regime. More precisely, there exists a critical value, if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value, then there exists a unique smooth subsonic compressible collision flow. And furthermore, there exists a smooth interface which separates the two non-miscible compressible subsonic flows. In particular, a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles. Finally, we showed some monotonic relationship between the location of the interface and the incoming mass fluxes.