Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Growth of high Sobolev Norms of solutions to the
  Zakharov-Kuznetsov Equation   We consider the Zakharov-Kuznetsov equation (ZK) in space dimension 2.
Solutions u with initial data u\_0 $\in$ H s are known to be global if s $\ge$
1. We prove that for any integer s $\ge$ 2, u(t) H s grows at most polynomially
in t for large times t. This result is related to wave turbulence and how a
solution of (ZK) can move energy to high frequencies. It is inspired by
analoguous results by Staffilani on the non linear Schr{\"o}dinger
Korteweg-de-Vries equation. The main ingredients are adequate bilinear
estimates in the context of Bourgain's spaces.

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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph