Uniqueness and instability of subsonic–sonic potential flow in a convergent approximate nozzle
Pan Liu, Hairong Yuan · Proceedings of the American Mathematical Society · 2010
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.