Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic Lp estimates by R-boundedness: Applications to the
  Navier-Stokes equations   General evolution equations in Banach spaces are investigated. Based on an
operator-valued version of de Leeuw's transference principle, time-periodic
$L^p$ estimates of maximal regularity type are established from
$\mathscr{R}$-bounds of the family of solution operators
($\mathscr{R}$-solvers) to the corresponding resolvent problems. With this
method, existence of time-periodic solutions to the Navier-Stokes equations is
shown for two configurations: in a periodically moving bounded domain and in an
exterior domain, subject to prescribed time-periodic forcing and boundary data.

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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga