  In this paper, we consider global weak solutions to com-pressible
Navier-Stokes-Korteweg equations with density dependent viscosities , in a
periodic domain $\Omega = \mathbb T^3$, with a linear drag term with respect to
the velocity. The main result concerns the exponential decay to equilibrium of
such solutions using log-sobolev type inequalities. In order to show such a
result, the starting point is a global weak-entropy solutions definition
introduced in D. Bresch, A. Vasseur and C. Yu [12]. Assuming extra assumptions
on the shear viscosity when the density is close to vacuum and when the density
tends to infinity, we conclude the exponential decay to equilibrium. Note that
our result covers the quantum Navier-Stokes system with a drag term.
