Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similar motions and related relative equilibria in the $N$-point
  vortex system   We study self-similar solutions of the point-vortex system. The explicit
formula for self-similar solutions has been obtained for the three point-vortex
problem and for a specific example of the four and five point-vortex problems.
We see that the families consisting of these self-similar collapsing solutions
are described by one-parameter families, and their collapse time and
Hamiltonian are also expressed by functions of the same parameter. Then, the
configurations at limit points of the parameter are in relative equilibria. For
the many-vortex problem, we investigate the point-vortex system with the help
of numerical computations. In particular, considering the case that $N - 1$
point vortices have a uniform vortex strength, we show that families of
self-similar collapsing solutions continuously depend on the Hamiltonian and
the self-similar solutions asymptotically approach relative equilibria as the
Hamiltonian gets close to certain values. In addition, we prove the existence
of relative equilibria for the four point-vortex system. We also investigate an
example of seven point vortices with non-uniform vortex strengths and give
numerical results for it.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas