Uniqueness and Instability of Subsonic--Sonic Potential Flow in A Convergent Approximate Nozzle

TL;DR

This paper establishes the uniqueness and instability of symmetric subsonic--sonic potential flows in convergent nozzles, providing mathematical insights into the behavior of compressible flows in aerodynamic surfaces.

Contribution

It proves the uniqueness and instability of subsonic--sonic flow solutions in convergent nozzles, using maximum principles and a generalized Hopf lemma.

Findings

Proved uniqueness of symmetric subsonic--sonic flow solutions.

Established instability of these flow solutions.

Developed a generalized Hopf boundary point lemma.

Abstract

We proved uniqueness and instability of the symmetric subsonic--sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross--sections. Such a surface may be regarded as an approximation of a two--dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation with Bernoulli type boundary conditions. The proof depends on maximum principles and a generalized Hopf boundary point lemma which was proved in the paper.