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Transactions of the American Mathematical Society

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Subsonic divided gas flow in an infinitely long branching channel


Authors: Jianfeng Cheng and Lili Du
Journal: Trans. Amer. Math. Soc. 371 (2019), 1859-1885
MSC (2010): Primary 76N10, 76G25, 35Q31, 35J25
DOI: https://doi.org/10.1090/tran/7403
Published electronically: October 23, 2018
MathSciNet review: 3894037
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Abstract: This paper deals with the compressible subsonic flows in an infinitely long asymmetric branching channel with two exhaust ducts. The flow satisfies the slip boundary conditions on the nozzle walls, and the total mass flux is prescribed in the inlet of the nozzle. We first established the existence of smooth subsonic irrotational flows through the branching channel for given sufficiently small total mass flux in the inlet. Several results on uniqueness are also obtained. In particular, imposing the location of the branching point on the nose of the channel, the uniqueness and the asymptotic behavior of the subsonic flow in upstream and downstream are shown, provided that the total mass flux is less than some critical value. Due to the asymmetric geometrics, the location of the branching point of the fluids has to be considered here. Of particular interest, it is observed that the location of the branching point on the nozzle wall is monotonic and continuously dependent on the ratio of the mass fluxes in the two exhaust ducts, and the branching point is the unique stagnation point in the fluid field and its closure. Finally, as a direct application, some results on subsonic-sonic divided flows are established.


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Additional Information

Jianfeng Cheng
Affiliation: Department of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
Email: jianfengcheng@126.com

Lili Du
Affiliation: Department of Mathematics and State Key Laboratory of Hydraulics and Mt River Engineering, Sichuan University, Chengdu 610064, People’s Republic of China
Email: dulili@scu.edu.cn

DOI: https://doi.org/10.1090/tran/7403
Keywords: Compressible subsonic flow, Euler system, branching point, existence and uniqueness
Received by editor(s): December 8, 2016
Received by editor(s) in revised form: July 7, 2017
Published electronically: October 23, 2018
Additional Notes: This work was supported in part by NSFC grants 11571243 and 11622105.
The second author is the corresponding author.
Article copyright: © Copyright 2018 American Mathematical Society