Global strong solutions for viscous radiative gas with degenerate temperature dependent heat conductivity in one-dimensional unbounded domains

Abstract

In one-dimensional unbounded domains, we prove the global existence of strong solutions to the compressible Navier–Stokes system for a viscous radiative gas, when the viscosity μ is a constant and the heat conductivity κ is a power function of the temperature θ according to κ(θ)=κ̃θβ, with β ≥ 0 and κ̃>0. Our result generalizes Zhao and Liao’s result [Y. K. Liao and H. J. Zhao, J. Differ. Equations 265, 2076–2120 (2018)] to the degenerate and nonlinear heat conductivity. In particular, the constant coefficients’ case (μ and κ are positive constants) is also covered in our theorem.