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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/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
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.