  We prove the ill-posedness of the 3-D baratropic Navier-Stokes equation for
the initial density and velocity belonging to the critical Besov space
$(\dot{B}^{\f 3p}_{p,1}+\bar{\rho},\,\dot{B}^{\f 3p-1}_{p,1})$ for $p>6$ in the
sense that a ``norm inflation" happens in finite time, here $\bar{\rho}$ is a
positive constant. Our argument also shows that the compressible viscous
heat-conductive flows is ill-posed for the initial density, velocity and
temperature belonging to the critical Besov space $(\dot{B}^{\f
3p}_{p,1}+\bar{\rho},\,\dot{B}^{\f 3p-1}_{p,1},\,\dot{B}^{\f 3p-2}_{p,1})$ for
$p>3$. These results shows that the compressible Navier-Stokes equations are
ill-posed in the smaller critical spaces compared with the incompressible
Navier-Stokes equations.
