Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cauchy's almost forgotten Lagrangian formulation of the Euler equation
  for 3D incompressible flow   Two prized papers, one by Augustin Cauchy in 1815, presented to the French
Academy and the other by Hermann Hankel in 1861, presented to G\"ottingen
University, contain major discoveries on vorticity dynamics whose impact is now
quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal
incompressible flow in terms of three invariants that generalize to three
dimensions the now well-known law of conservation of vorticity along fluid
particle trajectories for two-dimensional flow. This has very recently been
used to prove analyticity in time of fluid particle trajectories for 3D
incompressible Euler flow and can be extended to compressible flow, in
particular to cosmological dark matter. Hankel showed that Cauchy's formulation
gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux
invariants and, in the middle of the proof, derived an intermediate result
which is the conservation of the circulation of the velocity around a closed
contour moving with the fluid. This circulation theorem was to be rediscovered
independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were
only occasionally cited in the 19th century --- besides Hankel, foremost by
George Stokes and Maurice L\'evy --- and even less so in the 20th until they
were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed
to Cauchy only at the end of the 20th century by Russian scientists.

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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas