  In this paper we study existence of solutions for the Cauchy problem of the
Debye-H\"{u}ckel system with low regularity initial data. By using the
Chemin-Lerner time-space estimate for the heat equation, we prove that there
exists a unique local solution if the initial data belongs to the Besov space
$\dot{B}^{s}_{p,q}(\mathbb{R}^{n})$ for $-3/2<s\leq-2+\frac{n}{2}$,
$p=\frac{n}{s+2}$ and $1\leq q\leq \infty$, and furthermore, if the initial
data is sufficiently small then the solution is global. This result improves
the regularity index of the initial data space in previous results on this
model.
