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

2009/09/14 by Liu, Pan, Yuan, Hairong · 1 citation
#35B50 #35J70 #76H05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0909.2557

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.

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