A DEGENERATE ELLIPTIC PROBLEM FROM SUBSONIC-SONIC FLOWS IN CONVERGENT NOZZLES

This paper concerns continuous subsonic-sonic potential flows in a two dimensional convergent nozzle, which is governed by a free boundary problem of a quasilinear degenerate elliptic equation. It is shown that for a given nozzle which is a perturbation of an straight one, and a given mass flux, there exists uniquely a continuous subsonic-sonic flow whose velocity vector is along the normal direction at the inlet and the sonic curve. Furthermore, the sonic curve of this flow is a free boundary, where the flow is singular in the sense that the speed is only C-1/2 Holder continuous and the acceleration blows up at the sonic state.

Automated summary

This paper examines continuous subsonic-sonic potential flows in a two-dimensional converging nozzle, demonstrating the existence of a unique flow state with certain characteristics given a specific nozzle and mass flux. The study highlights the singular nature of the flow near the sonic state, where velocity is Holder continuous and acceleration diverges.