  In this paper we consider the Quantum Navier-Stokes system both in two and in
three space dimensions and prove global existence of finite energy weak
solutions for large initial data. In particular, the notion of weak solutions
is the standard one. This means that the vacuum region are included in the weak
formulations. In particular, no extra term like damping or cold pressure are
added to the system in order to define the velocity field in the vacuum region.
The main contribution of this paper is the construction of a regular
approximating system consistent with the effective velocity transformation
needed to get necessary a priori estimates.
