Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schr\"odinger equation on four-dimensional compact manifolds   We prove two new results about the Cauchy problem for nonlinear Schroedinger
equations on four-dimensional compact manifolds. The first one concerns global
wellposedness for Hartree-type nonlinearities and includes approximations of
cubic NLS on the sphere. The second one provides local wellposedness for
quadratic nonlinearities in the case of zonal data on the sphere. Both results
are based on new multilinear Strichartz-type estimates for the Schroedinger
group.

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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol