Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stokes operator in two-dimensional bounded Lipschitz domains   We consider the Stokes resolvent problem in a two-dimensional bounded
Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions.
We prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying $\lvert 1 / p -
1 / 2 \rvert < 1 / 4 + \varepsilon$ for some $\varepsilon > 0$. We further show
that the Stokes operator admits the property of maximal regularity and that its
$\mathrm{H}^{\infty}$-calculus is bounded. This is then used to characterize
domains of fractional powers of the Stokes operator. Finally, we give an
application to the regularity theory of weak solutions to the Navier-Stokes
equations in bounded planar Lipschitz domains.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an