Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Equilibrium Solutions For the Aggregation Equation with
  Power-Law Potentials   Despite their wide presence in various models in the study of collective
behaviors, explicit swarming patterns are difficult to obtain. In this paper,
special stationary solutions of the aggregation equation with power-law kernels
are constructed by inverting Fredholm integral operators or by employing
certain integral identities. These solutions are expected to be the global
energy stable equilibria and to characterize the generic behaviors of
stationary solutions for more general interactions.

10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph