  The Euler-Maxwell system as a hydrodynamic model for plasma physics to
describe the dynamics of the compressible electrons in a constant charged
non-moving ion background is studied. The global smooth flow with small
amplitude is constructed in three space dimensions when the electron velocity
relaxation is present. The speed of the electrons flow trending to uniform
equilibrium is obtained. The pointwise behavior of solutions to the linearized
homogeneous system in the frequency space is also investigated in detail.
