Stability of global strong solutions for the Cauchy problem of a vscous radiative and reactive gas model with temperature-dependent viscosity

This paper concerns the Cauchy problem for a viscous radiative and reactive gas model with temperature-dependent viscosity and heat-conductivity. We study the global existence and stability of strong solutions to the system in one-dimensional whole space. Specifically, we first obtain the time-uniform global existence of strong solutions under the assumption that the equations of state for pressure and specific internal energy satisfy the Stefan-Boltzmann law, with viscosity $\mu(\theta)=\theta^\alpha$ and heat conductivity $\kappa(\theta)=\widetilde{\kappa}(1+ \left.\theta^\beta\right)$. Furthermore, the asymptotic stability is also established for the global strong solutions with arbitrarily large initial data. Notably, the requirement on $\beta$ is substantially relaxed here to $\beta>\frac{3}{2}$, improving on the results of Liao and Zhao (J. Differential Equations, 2018).