Global Existence of Weak Solutions to the Three-Dimensional Full Compressible Quantum Equations

Abstract

We consider the quantum Navier-Stokes equations for the viscous, compressible, heat conducting fluids on the three-dimensional torus $T^3.$ The model is based on a system which is derived by Jungel, Matthes and Milisic [15]. We made some adjustment about the relation of the viscosities of quantum terms. The viscosities and the heat conductivity coefficient are allowed to depend on the density, and may vanish on the vacuum. By several levels of approximation we prove the global-in-time existence of weak solutions for the large initial data.