Uniform existence of the 1-D full equations for a thermo-radiative electromagnetic fluid

In this paper, we prove the uniform estimates with respect to the dielectric constant and the global-in-time existence of the 1-D full equations for a thermo-radiative electromagnetic fluid in a bounded interval without vacuum. We establish the uniform estimates in the dielectric constant, which gives that, as the dielectric constant tends to zero, the solutions to the 1-D full thermo-radiative electromagnetic equations will converge to the one for the 1-D full magnetohydrodynamic equations with thermo-radiations and magnetic diffusions. This approximation is usually referred to as the magnetohydrodynamic approximation, where the displacement current is not taken into account.