Global existence of weak solutions for generalized quantum MHD equation
  We prove the existence of a weak solution to a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent \gamma>1. 
Boling Guo, Binqiang Xie
math.AP