Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moffatt vortices: Concerns and Finiteness   Till date, the sequence of vortices present in the solid corners of steady
internal viscous incompressible flows, widely known as Moffatt vortices was
thought to be infinite. However, the already existing and most recent geometric
theories on incompressible viscous flows that express vortical structures in
terms of critical points in bounded domains, indicate a strong opposition to
this notion of infiniteness. In this study, we endeavor to bridge the gap
between the two opposing stream of thoughts by addressing what might have gone
wrong and pinpoint the shortcomings on the assumptions of the existing theorems
on Moffatt vortices. We provide our own set of proofs for establishing the
finiteness of the sequence of Moffatt vortices by making use of the continuum
hypothesis and Kolmogorov scale, which guarantee a non-zero scale for the
smallest vortex structure possible in incompressible viscous flows. We point
out that the notion of infiniteness resulting from discrete self-similarity of
the vortex structures is not physically feasible. The centers of these vortices
have been quantified by us as fixed points through Brouwer fixed-point theorem
and boundary of a vortex as circle cell. With the aid of these new developments
and making use of some existing theorems in topology along with some elementary
concept of mathematical analysis, we provide several approaches to delve into
this issue. All these approaches converge to the same conclusion that the
sequence of Moffatt vortices cannot be infinite; in fact, it is at most finite.

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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex