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Existence of periodic solutions to an isothermal relativistic Euler system

Abstract

In this paper, we study the global existence of periodic solutions to an isothermal relativistic Euler system in BV space. First, we analyze some properties of the shock and rarefaction wave curves in the Riemann invariant plane. Based on these properties, we construct the approximate solutions of the isothermal relativistic Euler system with periodic initial data by using a Glimm scheme, and prove that there exists an entropy solution V(x, t) which belongs to L ∩ BVloc (ℝ × ℝ+).

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Correspondence to Fei Wu.

Additional information

The work was supported by NSFC (11671193) and the Fundamental Research Funds for the Central Universities NE2015005.

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Wu, F., Wang, Z. Existence of periodic solutions to an isothermal relativistic Euler system. Acta Math Sci 42, 155–171 (2022). https://doi.org/10.1007/s10473-022-0108-x

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  • DOI: https://doi.org/10.1007/s10473-022-0108-x

Key words

  • isothermal relativistic Euler system
  • Glimm scheme
  • Riemann problem
  • BV space
  • periodicity

2010 MR Subject Classification

  • 76Y05
  • 35L65
  • 74J40
  • 35B10
  • 35A30