Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Zakharov system in 4D radial energy space below the ground state   We prove dynamical dichotomy into scattering and blow-up (in a weak sense)
for all radial solutions of the Zakharov system in the energy space of four
spatial dimensions that have less energy than the ground state, which is
written using the Aubin-Talenti function. The dichotomy is characterized by the
critical mass of the wave component of the ground state. The result is similar
to that by Kenig and Merle for the energy-critical nonlinear Schrodinger
equation (NLS). Unlike NLS, however, the most difficult interaction in the
proof stems from the free wave component. In order to control it, the main
novel ingredient we develop in this paper is a uniform global Strichartz
estimate for the linear Schrodinger equation with a potential of subcritical
mass solving a wave equation. This estimate, as well as the proof, may be of
independent interest. For the scattering proof, we follow the idea by Dodson
and Murphy.

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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: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex