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Delta shocks in the relativistic full Euler equations for a Chaplygin gas

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Zhiqiang Shao

Analysis of PDEs · Submitted 25 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Under the generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solutions are also established.

how it is stated · asserted 1.00 read the record →

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arXiv ID1709.08445 (version 1)
Pith IDOCHEZ3MY, Pith's permanent record of this paper and its review
CitationZhiqiang Shao. "Delta shocks in the relativistic full Euler equations for a Chaplygin gas." arXiv:1709.08445 (2017). https://pith.science/paper/OCHEZ3MY
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,837 input tokens.

What the abstract itself states, as probabilities: claims first 0.16 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.94 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The relativistic full Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are two kinds of Riemann solutions, in which one consists of three contact discontinuities and the other involves a delta shock wave on which both state variables the rest mass density and the proper energy density simultaneously contain the Dirac delta functions. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solutions are also established.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The relativistic full Euler equations for a Chaplygin gas are studied. background 0.64 0.68 0.03 asserted 0.90
s1 The Riemann problem is solved constructively. contribution 0.67 0.90 0.11 asserted 1.00
s2 There are two kinds of Riemann solutions, in which one consists of three contact discontinuities and the other involves a delta shock wave on which both state variables the rest mass density and the proper energy density simultaneously contain the Dirac delta functions. result 0.98 0.90 0.55 asserted 1.00
s3 It is quite different from the previous ones on which only one state variable contains the Dirac delta function. result 0.35 0.29 0.13 asserted 1.00
s4 The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. contribution 0.86 0.90 0.21 asserted 1.00
s5 Under the generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solutions are also established. result 0.85 0.92 0.38 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The relativistic full Euler equations for a Chaplygin gas are studied. The Riemann problem is solved constructively. There are two kinds of Riemann solutions, in which one consists of three contact discontinuities and the other involves a delta shock wave on which both state variables the rest mass density and the proper energy density simultaneously contain the Dirac delta functions. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solutions are also established.

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