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arXiv · 2609.24700

Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data

Hongyu Wang·Rong Zhang
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Abstract

We study the Cauchy problem for the one-dimensional full compressible Navier--Stokes equations with viscosity $μ(θ)=\tildeμθ^α$ and heat conductivity $κ(θ)=\tildeκθ^β$. For each fixed $β\ge0$, we prove the global stability of the combination of a viscous contact wave with rarefaction waves, provided that the viscosity exponent $α$ and the total wave strength are sufficiently small. The initial perturbation may be large in $H^1$, and the specific volume and temperature are assumed to have positive initial lower bounds. The solution remains uniformly bounded in $H^1$ relative to the wave, and converges uniformly to that wave as time tends to infinity. We show that both the specific volume and the temperature admit time-uniform lower and upper bound. Estimates for the logarithmic volume derivative and the temperature gradient then close the $H^1$ estimates without requiring a second derivative of the initial specific volume.

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Hongyu Wang, Rong Zhang. 2026-09-21. Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data. https://arxiv.org/abs/2609.24700

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