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PreprintCC BY 4.0arXiv

Long-Time Nonlinear Stability of Large-Amplitude Radial Rarefactive Flows for the Multidimensional Compressible Euler Equations

  • Faris El-Katri
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Abstract

In this paper, we study multidimensional perturbations of radially symmetric rarefactive flows for the compressible Euler equations. No assumptions on the smallness of the background are imposed. We derive lower bounds on both the classical lifespan and stability timespan of the perturbed solution. These lower bounds are demonstrated to tend to infinity as the size of the perturbation approaches zero. Furthermore, owing to the rarefactive nature of the background, the resulting estimate is shown to be substantially longer than the corresponding estimate for a general classical background with bounded first derivatives.

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Cite

BibTeXRIS
BibTeX
@misc{elkatri2026longtime,
  title = {{Long-Time Nonlinear Stability of Large-Amplitude Radial Rarefactive Flows for the Multidimensional Compressible Euler Equations}},
  author = {Faris El-Katri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04901},
  eprint = {2610.04901},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04901},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Long-Time Nonlinear Stability of Large-Amplitude Radial Rarefactive Flows for the Multidimensional Compressible Euler Equations
AU  - Faris El-Katri
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.04901
UR  - https://arxiv.org/abs/2610.04901
AB  - In this paper, we study multidimensional perturbations of radially symmetric rarefactive flows for the compressible Euler equations. No assumptions on the smallness of the background are imposed. We derive lower bounds on both the classical lifespan and stability timespan of the perturbed solution. These lower bounds are demonstrated to tend to infinity as the size of the perturbation approaches zero. Furthermore, owing to the rarefactive nature of the background, the resulting estimate is shown to be substantially longer than the corresponding estimate for a general classical background with bounded first derivatives.
ER  -