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

Authors:
Pan Liu and Hairong Yuan

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1793-1801

MSC (2010):
Primary 35J70, 35B50; Secondary 76H05

Published electronically:
January 7, 2010

MathSciNet review:
2587464

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Pan Liu**

Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China

Email:
pliu@math.ecnu.edu.cn

**Hairong Yuan**

Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China

Email:
hryuan@math.ecnu.edu.cn, hairongyuan0110@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-10-10202-0

Received by editor(s):
April 27, 2009

Received by editor(s) in revised form:
September 14, 2009

Published electronically:
January 7, 2010

Additional Notes:
The first author was supported in part by the National Science Foundation of China under Grants No. 10601017 and 10871126.

The second author (corresponding author) was supported in part by the National Science Foundation of China under Grant No. 10901052, Shanghai Chenguang Program (09CG20), a Special Research Fund for Selecting Excellent Young Teachers of the Universities in Shanghai sponsored by the Shanghai Municipal Education Commission, and the National Science Foundation (USA) under Grant DMS-0720925.

Communicated by:
Walter Craig

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.