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Transonic Shock Solutions to the Euler System in Divergent-Convergent Nozzles

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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.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Jilin University, Changchun, 130012, China

    Ben Duan

  2. School of Mathematics, Dalian University of Technology, Dalian, 116024, China

    Ao Lan

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Zhen Luo

Authors
  1. Ben Duan
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  2. Ao Lan
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  3. Zhen Luo
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Corresponding author

Correspondence to Zhen Luo.

Additional information

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).

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Duan, B., Lan, A. & Luo, Z. Transonic Shock Solutions to the Euler System in Divergent-Convergent Nozzles. Acta Math Sci 42, 1536–1546 (2022). https://doi.org/10.1007/s10473-022-0414-3

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  • DOI: https://doi.org/10.1007/s10473-022-0414-3

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