数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1536-1546.doi: 10.1007/s10473-022-0414-3

• 论文 • 上一篇    下一篇

TRANSONIC SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES

段犇1, 兰傲2, 罗珍3   

  1. 1. School of Mathematical Sciences, Jilin University, Changchun, 130012, China;
    2. School of Mathematics, Dalian University of Technology, Dalian, 116024, China;
    3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
  • 收稿日期:2021-02-20 修回日期:2021-05-24 出版日期:2022-08-25 发布日期:2022-08-23
  • 通讯作者: Zhen LUO,E-mail:zluo@xmu.edu.cn E-mail:zluo@xmu.edu.cn
  • 基金资助:
    The research of Ben Duan is partially supported by NSFC (11871133, 12171498). The research of Zhen Luo is partially supported by NSFC (11971402, 12171401) and the NSF of Fujian province, China (2020J01029).

TRANSONIC SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES

Ben DUAN1, Ao LAN2, Zhen LUO3   

  1. 1. School of Mathematical Sciences, Jilin University, Changchun, 130012, China;
    2. School of Mathematics, Dalian University of Technology, Dalian, 116024, China;
    3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
  • Received:2021-02-20 Revised:2021-05-24 Online:2022-08-25 Published:2022-08-23
  • Contact: Zhen LUO,E-mail:zluo@xmu.edu.cn E-mail:zluo@xmu.edu.cn
  • Supported by:
    The research of Ben Duan is partially supported by NSFC (11871133, 12171498). The research of Zhen Luo is partially supported by NSFC (11971402, 12171401) and the NSF of Fujian province, China (2020J01029).

摘要: In this paper, we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle. For a given physical supersonic inflow at the entrance, we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range. In addition, we establish the monotonicity between the location of the transonic shock and the pressure downstream.

关键词: Euler system, transonic shocks, steady solutions, nozzle

Abstract: In this paper, we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle. For a given physical supersonic inflow at the entrance, we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range. In addition, we establish the monotonicity between the location of the transonic shock and the pressure downstream.

Key words: Euler system, transonic shocks, steady solutions, nozzle

中图分类号: 

  • 35Q31