Uniqueness and instability of subsonic–sonic potential flow in a convergent approximate nozzle

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.