Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breaking of vortex lines - a new mechanism of collapse in hydrodynamics   A new mechanism of the collapse in hydrodynamics is suggested, due to
breaking of continuously distributed vortex lines. Collapse results in
formation of the point singularities of the vorticity field $|{\bf\Omega}|$. At
the collapse point, the value of the vorticity blows up as $(t_0-t)^{-1}$ where
$t_0$ is a collapse time. The spatial structure of the collapsing distribution
approaches a pancake form: contraction occurs by the law $l_1\sim(t_0-t)^{3/2}$
along the "soft" direction, the characteristic scales vanish like
$l_2\sim(t_0-t)^{1/2}$ along two other ("hard") directions. This scenario of
the collapse is shown to take place in the integrable three-dimensional
hydrodynamics with the Hamiltonian ${\cal H}=\int|{\bf\Omega}|d{\bf r}$. Most
numerical studies of collapse in the Euler equation are in a good agreement
with the proposed theory.

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The categories of this paper are: math
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol