A remark on the global existence of weak solutions to the compressible quantum Navier-Stokes equations

In this paper, we obtain the global existence of weak solutions to the compressible quantum Navier-Stokes equations. By virtue of a useful identity and an interesting estimate, we solve the critical case that the viscosity equals the dispersive coefficient. This result removes the restrictions on the coefficients and improves the recent work of Antonell and Spirito (2017) in some senses.