  In this paper, we consider the $3$D compressible radiation hydrodynamic (RHD)
equations with thermal conductivity in a bounded domain. The existence of
unique local strong solutions is firstly established when the initial data are
arbitrarily large and satisfy some initial layer compatibility condition. The
initial mass density needs not be bounded away from zero and may vanish in some
open set. Moreover, we show that if the initial vacuum domain is not so
irregular, then the compatibility condition is necessary and sufficient to
guarantee the existence of the unique strong solution. Finally, we show a
Beal-Kato-Majda type blow-up criterion in terms of $(\nabla I,\rho,\theta)$.
