Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Nonexistence of global weak solution with only one stable supersonic conic shock wave for the steady supersonic Euler flow past a perturbed cone


Authors: Xu Gang and Yin Huicheng
Journal: Quart. Appl. Math. 70 (2012), 199-218
MSC (2010): Primary 35L70, 35L65, 35L67, 76N15
DOI: https://doi.org/10.1090/S0033-569X-2012-01279-8
Published electronically: February 2, 2012
MathSciNet review: 2953100
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, for the potential equation, a global stable weak solution with only one conic shock wave has been established in some references. However, in contrast to the case of the potential equation, due to the essential influence of the rotations for the Euler flow, in this paper we will show that the global weak solution of the Euler system with one stable supersonic conic shock wave does not exist when a uniform supersonic incoming flow hits an infinitely long and curved sharp conic body.


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Additional Information

Xu Gang
Affiliation: Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China
Email: gxu@ujs.edu.cn

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

DOI: https://doi.org/10.1090/S0033-569X-2012-01279-8
Keywords: Supersonic flow, conic shock, full Euler system, stream line, nonexistence.
Received by editor(s): February 12, 2010
Published electronically: February 2, 2012
Additional Notes: This project is supported by the National Natural Science Foundation of China (Nos.10931007, 10871096, 11025105), the Doctorial Program Foundation of Ministry of Education of China (No.20090091110005) and Natural Science Foundation of Jiangsu province (10KJB110002).
Article copyright: © Copyright 2012 Brown University

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