Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data

Hongyu Wang; Rong Zhang

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arXiv · 2609.24435

Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data

Hongyu Wang·Rong Zhang

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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 $θ^α$ and $θ^β$, respectively. For every fixed $β\geq0$ and sufficiently small $α\geq0$, 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.

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BibTeX RIS

Hongyu Wang, Rong Zhang. 2026-09-21. Initial and initial boundary value problems for the Navier-Stokes equations with temperature-dependent transport coefficients and large data. https://arxiv.org/abs/2609.24435

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