Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vortex patches choreography for active scalar equations   This paper deals with the existence of $N$ vortex patches located at the
vertex of a regular polygon with $N$ sides that rotate around the center of the
polygon at a constant angular velocity. That is done for Euler and
(SQG)$_\beta$ equations, with $\beta\in(0,1)$, but may be also extended to more
general models. The idea is the desingularization of the Thomsom polygon for
the $N$ point vortex system, that is, $N$ point vortices located at the vertex
of a regular polygon with $N$ sides. The proof is based on the study of the
contour dynamics equation combined with the application of the infinite
dimensional Implicit Function theorem and the well--chosen of the function
spaces.

5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph