GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER-MAXWELL SYSTEM. THE RELAXATION CASE

The Euler-Maxwell system regarded as a hydrodynamic model for plasma physics describes the dynamics of 'compressible electrons' in a constant, charged, non-moving ion background. A global smooth flow with small amplitude is constructed here in three space dimensions when the electron velocity relaxation is taken into account. The speed of the electron flow tending to a uniform equilibrium, and the pointwise behavior of solutions to the linearized homogeneous system in the frequency space are investigated in detail.