  In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion
system. We obtain global well-posedness for the system in dimension $d=2$ for
any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times
H^{s_2}(\mathbb{R}^2)$ under certain conditions of $s_1$ and $s_2$.
