  In this paper we consider the Navier-Stokes-Korteweg equations for a viscous
compressible fluid with capillarity effects in three space dimensions. We prove
compactness of finite energy weak solutions for large initial data. In contrast
with previous results regarding this system, vacuum regions are allowed in the
definition of weak solutions and no additional damping terms are considered.
The compactness is obtained by introducing suitable truncations of the velocity
field and the mass density at different scales and use only the a priori bounds
obtained by the energy and the BD entropy.
