  The classical solution of the 3-D radiative hydrodynamics model is studied in
$H^k$-norm under two different conditions, with and without heat conductivity.
We have proved the following results in both cases. First, when the $H^k$ norm
of the initial perturbation around a constant state is sufficiently small and
the integer $k\geq2$, a unique classical solution to such Cauchy problem is
shown to exist. Second, if we further assume that the $L^1$ norm of the initial
perturbation is small too, the i-order($0\leq i\leq k-2$) derivative of the
solutions have the decay rate of $(1+t)^{-\frac 34-\frac i2}$ in $H^2$ norm.
Third, from the results above we can see that for radiative hydrodynamics, the
radiation can do the same job as the heat conduction, which means if the
thermal conductivity coefficient turns to $0$, because of the effect of
radiation, the solvability of the system and decay rate of the solution stay
the same.
