Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global solutions for the generalized Boussinesq equation in low-order
  Sobolev spaces   We show that the Cauchy problem for the defocusing generalized Boussinesq
equation $u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u)_{xx}=0$, $k\geq1$, on the real
line is globally well-posed in $H^{s}(\R)$ for $s>1-({1}/{3k})$. We use the
"$I$-method" to define a modification of the energy functional that is "almost
conserved" in time. Our result extends the previous one obtained by Farah and
Linares (2010 \textit{J. London Math. Soc.} \textbf{81} 241-254) when $k=1$.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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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: nucl-th
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The categories of this paper are: cmp-lg