Global Classical Large Solutions for the Initial Boundary Value Problem of the Radiation Hydrodynamics Model

ABSTRACT This paper is concerned with the global classical large solutions for the initial boundary value problem of the radiation hydrodynamics model with viscosity and thermal conductivity. The boundary conditions contain two cases: the periodic boundary conditions and the general boundary conditions: The key point is to derive strictly positive bounds for the density and temperature , which is more complex than the Navier–Stokes equations due to the influence of radiative heat flux. To overcome these difficulties, Zhang and Zhao in (2023) firstly constructed a pointwise estimate between the radiative heat flux and temperature using the method of Fourier analysis. And this pointwise estimate is extremely important to obtain the lower bound of the temperature . However, due to the technical limitations, Zhang and Zhao can only consider the case of periodic boundary conditions and special heat conductivity: (). For the general boundary conditions, we construct a same pointwise estimate between and by analyzing the equation about the radiation heat flux. Besides, we consider a general coefficient of heat conduction: if ; if , which extends the result in Zhang and Zhao in (2023), and also contains some important situations in physics that Zhang and Zhao in (2023) excludes. As a byproduct of our approach, the argument in Wen and Zhu (2013) is also extended to the more general for Navier–Stokes equations with large initial data.