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Spectral stability for strong ideal-gas shock layers
Abstract
We give a purely analytical proof of one-dimensional spectral stability of sufficiently strong shock layers for the full ideal-gas Navier--Stokes equations with constant viscosity and heat conduction. Earlier work reduced this question to a limiting problem and gave numerical evidence of stability, but no proof. We prove stability on an explicit region of gas constants and transport ratios that includes air and monatomic gases. No step of the argument relies on numerical computation, and the arguments, taking the cited results of Humpherys, Lyng, and Zumbrun as hypotheses, have also been verified in the Lean proof assistant.
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BibTeX
@misc{humpherys2026spectral,
title = {{Spectral stability for strong ideal-gas shock layers}},
author = {Jeffrey Humpherys},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22660},
eprint = {2610.22660},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22660},
}
RIS
TY - UNPB
TI - Spectral stability for strong ideal-gas shock layers
AU - Jeffrey Humpherys
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22660
UR - https://arxiv.org/abs/2610.22660
AB - We give a purely analytical proof of one-dimensional spectral stability of sufficiently strong shock layers for the full ideal-gas Navier--Stokes equations with constant viscosity and heat conduction. Earlier work reduced this question to a limiting problem and gave numerical evidence of stability, but no proof. We prove stability on an explicit region of gas constants and transport ratios that includes air and monatomic gases. No step of the argument relies on numerical computation, and the arguments, taking the cited results of Humpherys, Lyng, and Zumbrun as hypotheses, have also been verified in the Lean proof assistant.
ER -