Global Weak Solutions to a Three-Dimensional Quantum Kinetic-Fluid Model

In this paper, we study a quantum kinetic-fluid model in a three-dimensional torus. This model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity. We establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form p ( ρ ) = ρ γ + p c ( ρ ), where γ > 1 is the adiabatic coefficient and p c ( ρ ) satisfies for k ≥ 4 and some constant c > 0.