  This paper investigates the Cauchy problem of two-dimensional full
compressible Navier-Stokes system with density and temperature vanishing at
infinity. For the strong solutions, some a priori weighted $L^2(R^2)$-norm of
the gradient of velocity is obtained by the techniques of $A_p$ weights and
cancellation of singularity. Based on this key weighted estimate and some basic
weighted analysis of velocity and temperature, we establish the local existence
and uniqueness of strong solutions with initial vacuum by means of a two-level
approximation scheme. Meanwhile, for $q_1$ and $q_2$ as in (1.8), the
$L^\infty_tL^{q_1}_x$-norm of velocity and the $L^2_tL^{q_2}_x$-norm of
temperature are derived originally. Moreover, we obtain a blowup criterion only
in terms of the temporal integral of the maximum norm of divergence of
velocity, which is independent of the temperature.
