Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of Sobolev norms for the analytic NLS on $\mathbb T^2$   We consider the completely resonant defocusing non-linear Schr\"odinger
equation on the two dimensional torus with any analytic gauge invariant
nonlinearity. Fix $s>1$. We show the existence of solutions of this equation
which achieve arbitrarily large growth of $H^s$ Sobolev norms. We also give
estimates for the time required to attain this growth.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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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: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol