Global weak solution to the degenerate quantum Navier‐Stokes‐Maxwell equations with damping term

Abstract

In this paper we investigate the global existence of the finite energy weak solution to the isentropic quantum Navier-Stokes-Maxwell equations with density-dependent viscosity and the damping term in three-dimensional periodic domain. This model is composed of the isentropic compressible Navier-Stokes-Maxwell equation with density-dependent viscosity, the quantum Bohm potential and a damping term. This model can be used to describe the motion of the particle in the plasma under the electric-magnetic field. The main techniques are the Faedo-Galerkin method, some imbedding inequalities and some compactness theorems.