  In this paper, we study the well-posedness of Poisson-Nernst-Planck system
with no-flux boundary condition and singular permanent charges in two
dimension. The main difficulty comes from the lack of integrability of singular
permanent charges. In order to overcome the difficulty, the main idea is to
transform the system into another weighted parabolic system. By choosing
suitable weighted spaces, local existence of solutions can be obtained based on
a fixed-point argument. Moreover, we also proved global existence by energy
estimates under the smallness assumption on initial data.
