  The Euler-Poisson system is a fundamental two-fluid model to describe the
dynamics of the plasma consisting of compressible electrons and a uniform ion
background. In the 3D case Guo first constructed a global smooth irrotational
solution by using dispersive Klein-Gordon effect. It has been conjectured that
same results should hold in the two-dimensional case. In our recent work, we
proved the existence of a family of smooth solutions by constructing the wave
operators for the 2D system. In this work we completely settle the 2D Cauchy
problem.
