Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical justification of the point vortex dynamics in background
  fields on surfaces as an Euler-Arnold flow   The point vortex dynamics in background fields on surfaces is justified as an
Euler-Arnold flow in the sense of de Rham currents. We formulate a
current-valued solution of the Euler-Arnold equation with a regular-singular
decomposition. For the solution, we first prove that, if the singular part of
the vorticity is given by a linear combination of delta functions centered at
$q_n(t)$ for $n=1,\ldots,N$, $q_n(t)$ is a solution of the point vortex
equation. Conversely, we next prove that, if $q_n(t)$ is a solution of the
point vortex equation for $n=1,\ldots,N$, there exists a current-valued
solution of the Euler-Arnold equation with a regular-singular decomposition
such that the singular part of the vorticity is given by a linear combination
of delta functions centered at $q_n(t)$. As a corollary, we generalize the
Bernoulli law to the case where the flow field is a curved surface and where
the presence of point vortices is taken into account. From the viewpoint of the
application, the mathematical justification is of a significance since the
point vortex dynamics in the rotational vector field on the unit sphere is
adapted as a mathematical model of geophysical flow in order to take effect of
the Coriolis force on inviscid flows into consideration.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess