Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy conservation and blowup of solutions for focusing
  Gross-Pitaevskii hierarchies   We consider solutions of the focusing cubic and quintic Gross-Pitaevskii (GP)
hierarchies. We identify an observable corresponding to the average energy per
particle, and we prove that it is a conserved quantity. We prove that all
solutions to the focusing GP hierarchy at the $L^2$-critical or
$L^2$-supercritical level blow up in finite time if the energy per particle in
the initial condition is negative. Our results do not assume any factorization
of the initial data.

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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg