Global Existence and Decay of Solutions for the Bipolar Euler-Maxwell System in the Torus

The bipolar compressible Euler-Maxwell equations as a hydrodynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions was investigated. This work was concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions.With the help of energy method and the energy functional convex method, the global smooth solution with small amplitude was established near a constant equilibrium solution with asymptotic stability property.