TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

doi:10.1007/s10473-022-0416-1

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1569-1584.doi: 10.1007/s10473-022-0416-1

TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

翁上昆, 张子豪

School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

收稿日期:2021-03-04 修回日期:2021-05-23 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Zihao ZHANG,E-mail:zhangzihao@whu.edu.cn E-mail:zhangzihao@whu.edu.cn
基金资助:
The first author is partially supported by National Natural Science Foundation of China (11701431, 11971307, 12071359).

TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

Shangkun WENG, Zihao ZHANG

School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

Received:2021-03-04 Revised:2021-05-23 Online:2022-08-25 Published:2022-08-23
Contact: Zihao ZHANG,E-mail:zhangzihao@whu.edu.cn E-mail:zhangzihao@whu.edu.cn
Supported by:
The first author is partially supported by National Natural Science Foundation of China (11701431, 11971307, 12071359).

摘要/Abstract

摘要： In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation, which tends to a given radially symmetric subsonic spiral flow at far field. The optimal decay rate at far field is also derived by Kelvin’s transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compensated compactness framework.

关键词: Subsonic spiral flows, Euler equations, subsonic-sonic limit, a porous body

Abstract: In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation, which tends to a given radially symmetric subsonic spiral flow at far field. The optimal decay rate at far field is also derived by Kelvin’s transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compensated compactness framework.

Key words: Subsonic spiral flows, Euler equations, subsonic-sonic limit, a porous body

中图分类号:

35B40

翁上昆, 张子豪. TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY[J]. 数学物理学报(英文版), 2022, 42(4): 1569-1584.

Shangkun WENG, Zihao ZHANG. TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1569-1584.

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TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

TWO DIMENSIONAL SUBSONIC AND SUBSONIC-SONIC SPIRAL FLOWS OUTSIDE A POROUS BODY

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