Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A Liouville-type theorem for subsonic flows around an infinite long ramp


Authors: Yang Hui and Yin Huicheng
Journal: Quart. Appl. Math. 72 (2014), 253-265
MSC (2010): Primary 35L70, 35L65, 35L67, 76N15
DOI: https://doi.org/10.1090/S0033-569X-2014-01352-0
Published electronically: March 14, 2014
MathSciNet review: 3186235
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Abstract: In this paper, we focus on the two-dimensional subsonic flow problem for polytropic gases around an infinite long ramp, which is motivated by a description in Section 111 of Courant-Friedrichs' book Supersonic flow and shock waves. The flow is assumed to be steady, isentropic and irrotational; namely, the movement of the flow is described by a second-order steady potential equation. By the complex methods together with some properties on quasi-conformal mappings, we show that a nontrivial subsonic flow around the infinite long ramp does not exist if the flow is uniformly subsonic.


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Additional Information

Yang Hui
Affiliation: School of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, People’s Republic of China, and Department of Mathematics and IMS, Nanjing University, Nanjing 210093, People’s Republic of China
Email: yanghsj@ahut.edu.cn

Yin Huicheng
Affiliation: Department of Mathematics and IMS, Nanjing University, Nanjing 210093, People’s Republic of China
Email: huicheng@nju.edu.cn

DOI: https://doi.org/10.1090/S0033-569X-2014-01352-0
Keywords: Subsonic flow, potential equation, quasi-conformal, Riemann metric, ramp
Received by editor(s): May 26, 2012
Published electronically: March 14, 2014
Additional Notes: This research was supported by NSFC (No.11025105, No.10931007), the Doctorial Program Foundation of Ministry of Education of China (No.20090091110005), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Article copyright: © Copyright 2014 Brown University


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