Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness for the massive Maxwell-Klein-Gordon equation with
  small critical Sobolev data   In this paper we prove global well-posedness and modified scattering for the
massive Maxwell-Klein-Gordon equation in the Coulomb gauge on
$\mathbb{R}^{1+d}$ $(d \geq 4)$ for data with small critical Sobolev norm. This
extends to the general case $ m^2 > 0 $ the results of Krieger-Sterbenz-Tataru
($d=4,5 $) and Rodnianski-Tao ($ d \geq 6 $), who considered the case $ m=0$.
  We proceed by generalizing the global parametrix construction for the
covariant wave operator and the functional framework from the massless case to
the Klein-Gordon setting. The equation exhibits a trilinear cancelation
structure identified by Machedon-Sterbenz. To treat it one needs sharp $ L^2 $
null form bounds, which we prove by estimating renormalized solutions in null
frames spaces similar to the ones considered by Bejenaru-Herr. To overcome
logarithmic divergences we rely on an embedding property of $ \Box^{-1} $ in
conjunction with endpoint Strichartz estimates in Lorentz spaces.

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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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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: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: supr-con