Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of perimeter for vortex patches in a bulk   We consider the two-dimensional incompressible Euler equations. We construct
vortex patches with smooth boundary on $T^2$ and $R^2$ whose perimeter grows
with time. More precisely, for any constant $M > 0$, we construct a vortex
patch in $T^2$ whose smooth boundary has length of order 1 at the initial time
such that the perimeter grows up to the given constant $M$ within finite time.
The construction is done by cutting a thin stick out of an almost square patch.
A similar result holds for an almost round patch with a thin handle in $R^2$.

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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an