Global existence and asymptotic behavior of the solutions to the three-dimensional bipolar Euler–Poisson systems

Abstract

In this paper, the global existence of smooth solutions for the three-dimensional bipolar hydrodynamic model is studied when the initial data are close to a constant state. The L 2 -decay rate of the solutions is also obtained. Our approach is based on the detailed analysis of the Green function of the linearized system and the elaborate energy estimates. As far as we known, it is the first result about the existence and L 2 -decay rate of global smooth solutions to the multi-dimensional bipolar hydrodynamic model.