Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gevrey regularity for the supercritical quasi-geostrophic equation   In this paper, following the techniques of Foias and Temam, we establish
suitable Gevrey class regularity of solutions to the supercritical
quasi-geostrophic equations in the whole space, with initial data in "critical"
Sobolev spaces. Moreover, the Gevrey class that we obtain is "near optimal" and
as a corollary, we obtain temporal decay rates of higher order Sobolev norms of
the solutions. Unlike the Navier-Stokes or the subcritical quasi-geostrophic
equations, the low dissipation poses a difficulty in establishing Gevrey
regularity. A new commutator estimate in Gevrey classes, involving the dyadic
Littlewood-Paley operators, is established that allow us to exploit the
cancellation properties of the equation and circumvent this difficulty.

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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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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: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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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: astro-ph