Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonnegative measures belonging to $H^{-1}(\mathbb{R}^2)$   Radon measures belonging to the negative Sobolev space $H^{-1}(\mathbb{R}^2)$
are important from the point of view of fluid mechanics as they model vorticity
of vortex-sheet solutions of incompressible Euler equations. In this note we
discuss regularity conditions sufficient for nonnegative Radon measures
supported on a line to be in $H^{-1}(\mathbb{R}^2)$. Applying the obtained
results, we derive consequences for measures on $\mathbb{R}^2$ with arbitrary
support and prove elementarily, among other things, that measures belonging to
$H^{-1}(\mathbb{R}^2)$ may be supported on a set of Hausdorff dimension $0$. We
comment on possible numerical applications.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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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: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th