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

@misc{wang2026global,
  title = {{Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data}},
  author = {Hongyu Wang and Rong Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24700},
  eprint = {2609.24700},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24700},
}

TY  - UNPB
TI  - Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data
AU  - Hongyu Wang
AU  - Rong Zhang
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24700
UR  - https://arxiv.org/abs/2609.24700
AB  - We study the Cauchy problem for the one-dimensional full compressible Navier--Stokes equations with viscosity μ(θ)=μ̃θ^α and heat conductivity κ(θ)=κ̃θ^β. For each fixed β≥0, 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.
ER  -