Existence of global steady subsonic Euler flows with collision through 2D infinitely long nozzles

Abstract

In this paper, we study the global existence of steady subsonic flows with collision, where the collision is caused by a confluence of two semi‐infinitely incoming flows that are nonmiscible steady subsonic irrotational Euler flows come from two different infinitely nozzles. First, we prove that when the total flux of two incoming flows is less that the critical mass flux, there exists a unique global smooth subsonic flow with collision. Meanwhile, the interface between two flows is a smooth free interface, which is determined uniquely by the mass fluxes of incoming flows. Second, by using the blowup argument, we establish the asymptotic behaviors for the stream function. Finally, we prove that the position of free interface can be determined uniquely by the mass fluxes of incoming flows. Moreover, we establish the monotonicity of the relation between the position of free interface and the mass fluxes of incoming flows.