Abstract: The radiative Euler equations is a typical model describing the motion of astrophysical flows. For its mathematical studies, it is now well-understood that the radiation effect can indeed induce some dissipative mechanism, which can guarantee the global regularity of smooth solutions to the radiative Euler equations for small initial data. Thus a problem of interest is to see to what extent does the viscosity and/or thermal conductivity influence the global regularity of smooth solutions to the one-dimensional radiative Euler equations for large initial data.
For results in this direction, it is shown in [30] that, for a class of state equations, even if a special class of thermal conductivity is further added to the radiative Euler equations, its smooth solutions will still blow up in finite time for large initial data. The main purpose of this paper focuses on the case when both viscosity and thermal conductivity are considered. We first show that, for the state equations and the heat conductivity considered in [30], if the viscosity is further taken into account, the corresponding radiative Navier-Stokes equations does admit a unique global smooth solution for any large initial data provided that the viscosity is a smooth function of the density satisfying certain growth conditions as the density tends to zero and infinity. Moreover, we also show that similar result still holds for the case when the thermodynamics variables satisfy the state equations for ideal polytropic gases, the heat conductivity takes the form studied in [30], and the viscosity is assumed to satisfy the same conditions imposed in the first result.

Key words: radiative Euler equations, radiative Navier-Stokes equations, constitutive relations for thermodynamics variables, ideal polytropic gases, transport coefficients, global smooth large solutions, global regularity