Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a conjugate point in the incompressible Euler flow on a
  three-dimensional ellipsoid   The existence of a conjugate point on the volume-preserving diffeomorphism
group of a compact Riemannian manifold M is related to the Lagrangian stability
of a solution of the incompressible Euler equation on M. The Misiolek curvature
is a reasonable criterion for the existence of a conjugate point on the
volume-preserving diffeomorphism group corresponding to a stationary solution
of the incompressible Euler equation. In this article, we introduce a class of
stationary solutions on an arbitrary Riemannian manifold whose behavior is nice
with respect to the Misiolek curvature and give a positivity result of the
Misiolek curvature for solutions belonging to this class. Moreover, we also
show the existence of a conjugate point in the three-dimensional ellipsoid case
as its corollary.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph