Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and well-posedness of 2D viscous shallow water system
  in Sobolev spaces with low regularity   In this paper we consider the Cauchy problem for 2D viscous shallow water
system in $H^s(\mathbb{R}^2)$, $s>1$. We first prove the local well-posedness
of this problem by using the Littlewood-Paley theory, the Bony decomposition,
and the theories of transport equations and transport diffusion equations.
Then, we get the global existence of the system with small initial data in
$H^s(\mathbb{R}^2)$, $s>1$. Our obtained result improves the recent result in
\cite{W}

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph