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

Abstract

In this paper, we proved the existence of global weak solutions of the compressible quantum Navier--Stokes equations with large data in three dimensions (3D). The model consists of the compressible Navier--Stokes equations with degenerate viscosity, a nonlinear third-order differential operator known as the quantum Bohm potential, and some damping terms. The global weak solution is shown by using the Faedo--Galerkin method and the compactness arguments. This system is also an approximation to the compressible Navier--Stokes equations. It will help us to prove the existence of global weak solutions to the compressible Navier--Stokes equations with degenerate viscosity in 3D.