Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global solvability and blow up for the convective Cahn-Hilliard
  equations with concave potentials   We study initial boundary value problems for the convective Cahn-Hilliard
equation $\Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0$. It is well-known that without
the convective term, the solutions of this equation may blow up in finite time
for any $p>0$. In contrast to that, we show that the presence of the convective
term $u\px u$ in the Cahn-Hilliard equation prevents blow up at least for
$0<p<\frac49$. We also show that the blowing up solutions still exist if $p$ is
large enough ($p\ge2$). The related equations like
Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard
equation, are also considered.

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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci