Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal gradient estimates and asymptotic behaviour for the
  Vlasov-Poisson system with small initial data   The Vlasov-Poisson system describes interacting systems of collisionless
particles. For solutions with small initial data in three dimensions it is
known that the spatial density of particles decays like $t^{-3}$ at late times.
In this paper this statement is refined to show that each derivative of the
density which is taken leads to an extra power of decay so that in $N$
dimensions for $N\ge 3$ the derivative of the density of order $k$ decays like
$t^{-N-k}$. An asymptotic formula for the solution at late times is also
obtained.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex