Quantum hydrodynamic (QHD) systems arise in the effective description of phenomena where quantistic behavior can be seen also at a macroscopic scale. This is the case for instance in Bose-Einstein condensation, superfluidity or in the modeling of semiconductor devices. Standard results for global existence of finite energy weak solutions to the QHD system often exploit the analogy with a nonlinear Schrödinger equation; by using the Madelung transform it is possible to define a solution to the QHD by considering the momenta (mass and current density) associated to a wave function. In particular this argument requires the initial data to be determined by a given wave function. This usual approach hence shows the existence of solutions but can not be used to study their stability properties in a general framework. In this talk I will present some recent developments that overcome those difficulties for the one dimensional QHD system. First of all I will provide an existence result for a large class of initial data, without requiring them to be generated by a wave function. Furthermore, I will prove a stability result for weak solutions. This exploits a novel functional which formally controls the L^2 norm of the chemical potential, weighted with the particle density. This is a joint work with P. Marcati and H. Zheng.