Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global classical solutions of the Vlasov-Fokker-Planck equation with
  local alignment forces   In this paper, we are concerned with the global well-posedness and
time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment
forces. The equation can be formally derived from an agent-based model for
self-organized dynamics which is called Motsch-Tadmor model with noises. We
present the global existence and uniqueness of classical solutions to the
equation around the global Maxwellian in the whole space. For the large-time
behavior, we show the algebraic decay rate of solutions towards the equilibrium
under suitable assumptions on the initial data. We also remark that the rate of
convergence is exponential when the spatial domain is periodic. The main
methods used in this paper are the classical energy estimates combined with
hyperbolic-parabolic dissipation arguments.

1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci