JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 55-65.doi: 10.6040/j.issn.1671-9352.0.2021.228

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Shadow wave solution for the relativistic Chaplygin Euler equations

JIA Yi-fei, GUO Li-hui*, BAI Yin-song   

  1. School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Published:2022-03-29

Abstract: The main purpose of this article is to construct the shadow wave solution of the relativistic Chaplygin Euler equations. To ensure the weak uniqueness of the shadow wave solution, the over-compressive entropy condition is used as the admissibility criteria. Finally, in the sense of Schwartz generalized function, it is proved that the over-compressive shadow wave solution converges to the delta shock wave solution.

Key words: relativistic Euler equations, Chaplygin gas, shadow wave, delta shock wave

CLC Number: 

  • O175.27
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