Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blowup behaviour for the nonlinear Klein--Gordon equation   We analyze the blowup behaviour of solutions to the focusing nonlinear
Klein--Gordon equation in spatial dimensions $d\geq 2$. We obtain upper bounds
on the blowup rate, both globally in space and in light cones. The results are
sharp in the conformal and sub-conformal cases. The argument relies on Lyapunov
functionals derived from the dilation identity. We also prove that the critical
Sobolev norm diverges near the blowup time.

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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph