  We consider the 3-D full Navier-Stokes equations whose the viscosity
coefficients and the thermal conductivity coefficient depend on the density and
the temperature. We prove the local existence and uniqueness of the strong
solution in a domain $\Omega\subset\mathbb{R}^3$. The initial density may
vanish in an open set and $\Omega$ could be a bounded or unbounded domain. We
also prove a blow-up criterion for the solution. Finally, we show the blow-up
of the smooth solution to the compressible Navier-Stokes equations in
$\mathbb{R}^n$ ($n\geq1$) when the initial density has compactly support and
the initial total momentum is nonzero.
