Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multipole vortex patch equilibria for active scalar equations   We study how a general configuration of finitely-many point vortices, in a
state of uniform rotation or translation with Newtonian interaction or
generalized surface quasi-geostrophic interactions, can be desingularized into
a steady configuration of vortex patches. Using a technique first introduced by
Hmidi and Mateu for vortex pairs, we reformulate the problem for the patch
boundaries so that it no longer appears singular, at which point classical
techniques such as Lyapunov--Schmidt reduction can be used. Provided the point
vortex equilibrium is non-degenerate in a natural sense, solutions can be
constructed directly using the implicit function theorem, yielding asymptotics
for the shape of the patch boundaries. As an application, we prove the
existence of various families of solutions with patches arranged in asymmetric
pairs, regular polygons, body-centered polygons, and nested regular polygons.
These configurations are degenerate due to their additional symmetries, but
this difficulty can be overcome by integrating the appropriate symmetries into
the formulation of the problem.

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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex