Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analyticity of dissipative-dispersive systems in higher dimensions   We investigate the analyticity of the attractors of a class of
Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions,
which are periodic in all spatial variables and possess a universal attractor.
This is done by fine-tuning the techniques used in a previous work of the
second author, which are based on an analytic extensibility criterion involving
the growth of $\nabla^n u$, as $n$ tends to infinity (here $u$ is the
solution). These techniques can now be utilised in a variety of higher
dimensional equations possessing universal attractors, including
Topper--Kawahara equation, Frenkel--Indireshkumar equations and their
dispersively modified analogs. We prove that the solutions are analytic
whenever $\gamma$, the order of dissipation of the pseudo-differential
operator, is higher than one. We believe that this estimate is optimal, based
on numerical evidence.

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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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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: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph