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Uniqueness and instability of subsonic-sonic potential flow in a convergent approximate nozzle
Author(s):
Pan
Liu;
Hairong
Yuan
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1793-1801.
MSC (2010):
Primary 35J70, 35B50;
Secondary 76H05
Posted:
January 7, 2010
MathSciNet review:
2587464
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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:
10.1090/S0002-9939-10-10202-0
PII:
S 0002-9939(10)10202-0
Received by editor(s):
April 27, 2009,
Received by editor(s) in revised form:
September 14, 2009
Posted:
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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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