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 $L^{\infty}\cap {\rm BV}_{\rm loc}(\mathbb{R}\times\mathbb{R}_+)$.
Fei WU
,
Zejun WANG
. EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM[J]. Acta mathematica scientia, Series B, 2022
, 42(1)
: 155
-171
.
DOI: 10.1007/s10473-022-0108-x
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