  In this paper we study global existence of weak solutions for the Quantum
Hydrodynamics System in 2-D in the space of energy. We do not require any
additional regularity and/or smallness assumptions on the initial data. Our
approach replaces the WKB formalism with a polar decomposition theory which is
not limited by the presence of vacuum regions. In this way we set up a self
consistent theory, based only on particle density and current density, which
does not need to define velocity fields in the nodal regions. The mathematical
techniques we use in this paper are based on uniform (with respect to the
approximating parameter) Strichartz estimates and the local smoothing property.
