Transonic shock solutions of the steady Euler flow in quasi-one-dimensional convergent nozzles

Abstract

In this paper, we investigate the well-posedness of transonic shock solutions of the steady Euler flow in quasi-one-dimensional convergent nozzles under the physical boundary conditions proposed by Courant-Friedrichs in [12]. Inspired by [20], for any supersonic incoming flow at the entrance, we derive the critical length of the nozzle and show that as long as the nozzle length is less than or equal to the critical length, the existence and uniqueness of transonic shock solutions with the exit pressure lying in a certain range can be obtained. Moreover, the transonic shock position is monotonically determined by the exit pressure.