Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on blow-up criteria for the derivative nonlinear Schrodinger
  equation under the optimal threshold setting   We study the Cauchy problem of the mass critical nonlinear Schrodinger
equation with derivative with the 4pi mass. One has the global well-posedness
in H^1 whenever "the mass is strictly less than 4pi" or whenever "the mass is
equal to 4pi and the momentum is strictly less than zero". In this paper, by
the concentration compact principle as originally done by Kenig-Merle, we
obtain the limiting profile of blow up solutions with the critical 4pi mass.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas