Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on ill-posedness for the KdV equation   We prove that the solution-map $ u_0 \mapsto u $ associated with the KdV
equation cannot be continuously extended in $ H^s(\R) $ for $ s<-1 $. The main
ingredients are the well-known Kato smoothing effect for the mKdV equation as
well as the Miura transform.

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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th