Global Existence of Finite Energy Weak Solutions of Quantum   Navier-Stokes Equations
  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. 
Paolo Antonelli and Stefano Spirito
math.AP