Global Weak Solutions to the Compressible Quantum Navier-Stokes Equations with Damping

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solutions to such system is shown by using the Faedo-Galerkin method and the compactness argument. This system is also a very important approximation to the compressible Navier-Stokes equations. It will help us to prove the existence of global weak solutions to the compressible NavierStokes equations with degenerate viscosity in three dimensional space.