Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of solutions to the Poisson--Nernst--Planck system with
  singular permanent charges in $\mathbb{R}^2$   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.

25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg