Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Humpherys, Jeffrey
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222971278