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Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data
Abstract
We consider initial and initial boundary value problems for the one-dimensional compressible Navier--Stokes equations of an ideal polytropic gas in unbounded domains. The viscosity and heat conductivity are proportional to θα and θβ, respectively. For every fixed β≥0 and sufficiently small α≥0, depending on the initial data, we prove the global existence and asymptotic stability of a strong solution for arbitrarily large H1 initial data. Dividing the momentum equation by the viscosity allows us to estimate the specific-volume derivative without an initial H2 assumption.
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BibTeX
@misc{wang2026initial,
title = {{Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data}},
author = {Hongyu Wang and Rong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24435},
eprint = {2609.24435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24435},
}
RIS
TY - UNPB
TI - Initial and initial boundary value problems for the Navier-Stokes equations 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.2609.24435
UR - https://arxiv.org/abs/2609.24435
AB - We consider initial and initial boundary value problems for the one-dimensional compressible Navier--Stokes equations of an ideal polytropic gas in unbounded domains. The viscosity and heat conductivity are proportional to θ^α and θ^β, respectively. For every fixed β≥0 and sufficiently small α≥0, depending on the initial data, we prove the global existence and asymptotic stability of a strong solution for arbitrarily large H^1 initial data. Dividing the momentum equation by the viscosity allows us to estimate the specific-volume derivative without an initial H^2 assumption.
ER -