Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ill-posedness for the two component Degasperis-Procesi equation in
  critical Besov space   In this paper, we study the Cauchy problem for the two component
Degasperis-Procesi equation in critical Besov space $B^1_{\infty,1}(\mathbb
R)$. By presenting a new construction of initial data, we proved the norm
inflation of the corresponding solutions in $B^1_{\infty,1}(\mathbb R)$ and
hence ill-posedness. This is quite different from the local well-posedness
result for the Degasperis-Procesi equation in critical Besov space
$B^1_{\infty,1}(\mathbb R)$ due to the coupled structure of density function.

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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom