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Long-Time Behavior towards Generic Riemann Solutions for Radiative Euler Equations

  • Jeffrey Cheng
  • Namhyun Eun
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Abstract

We study the time-asymptotic stability of generic Riemann solutions for the one-dimensional radiative Euler equations, where the Riemann pattern consists of a $1$-rarefaction wave, a $2$-contact discontinuity, and a $3$-shock wave. We prove that, for sufficiently small wave strengths and initial perturbations, the Cauchy problem admits a unique global solution, which converges uniformly as t→ ∞ to a composite wave of the $1$-rarefaction wave, $2$-viscous contact wave, and $3$-radiative shock profile with a time-dependent shift. As a key ingredient, we establish a comprehensive set of quantitative estimates for weak radiative shock profiles. Our proof is based on the method of a-contraction with shifts. In all previous applications of the a-contraction method to the study of long-time behavior, the proof has relied essentially on the parabolic structure provided by either viscosity or heat conduction. In this work, we extend the method to a hyperbolic-elliptic system without parabolic structure.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026longtime,
  title = {{Long-Time Behavior towards Generic Riemann Solutions for Radiative Euler Equations}},
  author = {Jeffrey Cheng and Namhyun Eun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41106},
  eprint = {2610.41106},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41106},
}
RIS
TY  - UNPB
TI  - Long-Time Behavior towards Generic Riemann Solutions for Radiative Euler Equations
AU  - Jeffrey Cheng
AU  - Namhyun Eun
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41106
UR  - https://arxiv.org/abs/2610.41106
AB  - We study the time-asymptotic stability of generic Riemann solutions for the one-dimensional radiative Euler equations, where the Riemann pattern consists of a $1$-rarefaction wave, a $2$-contact discontinuity, and a $3$-shock wave. We prove that, for sufficiently small wave strengths and initial perturbations, the Cauchy problem admits a unique global solution, which converges uniformly as t→ ∞ to a composite wave of the $1$-rarefaction wave, $2$-viscous contact wave, and $3$-radiative shock profile with a time-dependent shift. As a key ingredient, we establish a comprehensive set of quantitative estimates for weak radiative shock profiles. Our proof is based on the method of a-contraction with shifts. In all previous applications of the a-contraction method to the study of long-time behavior, the proof has relied essentially on the parabolic structure provided by either viscosity or heat conduction. In this work, we extend the method to a hyperbolic-elliptic system without parabolic structure.
ER  -