Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On geometry of the Lagrangian description of ideal fluids   The Euler equation for an inviscid, incompressible fluid in a
three-dimensional domain M implies that the vorticity is a frozen-in field.
This can be used to construct a symplectic structure on RxM. The normalized
vorticity and the suspended velocity fields are Hamiltonian with the function t
and the Bernoulli function, respectively. The symplectic structure incorporates
the helicity conservation law as an identity. The infinitesimal dilation for
the symplectic two-form can be interpreted as a current vector for the
helicity. The symplectic dilation implies the existence of contact
hypersurfaces. In particular, these include contact structures on the space of
streamlines and the Bernoulli surfaces. The symplectic structure on RxM can be
realized as symplectisations of these through the Euler equation.

26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th