Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness for a class of singular Vlasov equations   In this article we study a singular Vlasov system on the torus where the
force field has the smoothness of a (fractional) derivative $D^{\alpha}$ of the
density, where $\alpha>0$. We prove local well-posedness in Sobolev spaces
without restriction on the data. This is in sharp contrast with the case
$\alpha=0$ which is ill-posed in Sobolev spaces for general data.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th