Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propagation of moments and uniqueness of weak solutions to the
  Vlasov-Poisson-Fokker-Planck system   In this paper, we prove the uniqueness of weak solutions to the
Vlasov-Poisson-Fokker-Planck system in $C([0,T]; L^p)$, by assuming the
solution has a local bounded density which tends to infinite with a
"reasonable" rate as $t\to 0$. And particularly as a corollary, we get the
uniqueness of weak solutions with initial data $f_0$ satisfying $f_0|v|^2\in
L^1$, which solves the uniqueness of weak solutions with finite energy. In
addition, we prove that the moments with respect to the velocity propagate for
any order higher than 2.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph