  We consider the compressible Navier-Stokes-Korteweg system describing the
dynamics of a liquid-vapor mixture with diffuse interphase. The global
solutions are established under linear stability conditions in critical Besov
spaces. In particular, the sound speed may be greater than or equal to zero. By
fully exploiting the parabolic property of the linearized system for all
frequencies, we see that there is no loss of derivative usually induced by the
pressure for the standard isentropic compressible Navier-Stokes system. This
enables us to apply Banach's fixed point theorem to show the existence of
global solution. Furthermore, we obtain the optimal decay rates of the global
solutions in the $L^2(\mathbb{R}^d)$-framework.
