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

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

2009-09-14

arxiv.org/abs/0909.2557v1

Mathematics

Analysis of PDEs

9 pages

Scientific paper

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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