  The formation of singularity and breakdown of strong solutions to the
two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes
equations with zero heat conduction are considered. It is shown that for the
initial density allowing vacuum, the strong solution exists globally if the
density $\rho$ and the pressure $P$ satisfy
$\|\rho\|_{L^{\infty}(0,T;L^\infty)}+\|P\|_{L^{\infty}(0,T;L^\infty)}<\infty$.
In addition, the initial density can even have compact support. The
logarithm-type estimate for the Lam{\'e} system and some weighted estimates
play a crucial role in the proof.
