Existence of solutions for a viscous hybrid quantum system for arbitrary large current density

In this paper, we continue to analyse the properties of the hybrid model introduced in the works by Chiarelli et al. and Di Michele et al. In particular, we consider a quantum hybrid model with a special viscous functional, as introduced in the work by Gamba and Jungel, for the quantum hydrodynamical model in its standard form (QHD). We show that the hybrid QHD (H-QHD) model admits weak solutions also for arbitrary large value of the current density J under a suitable pressure function.