  In this paper, we consider the initial-boundary value problem to the
compressible Navier-Stokes equations for ideal gases without heat conduction in
the half space or outside a fixed ball in $\mathbb R^N$, with $N\geq1$. We
prove that any classical solutions $(\rho, u, \theta)$, in the class
$C^1([0,T]; H^m(\Omega))$, $m>[\frac N2]+2$, with bounded from below initial
entropy and compactly supported initial density, which allows to touch the
physical boundary, must blow-up in finite time, as long as the initial mass is
positive. This paper extends the classical reault by Xin [CPAM, 1998], in which
the Cauchy probelm is considered, to the case that with physical boundary.
