Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The gradient flow for entropy on closed planar curves   In this paper we consider the steepest descent $L^2$-gradient flow of the
entropy functional. The flow expands convex curves, with the radius of an
initial circle growing like the square root of time. Our main result is that,
for any initial curve (either immersed locally convex of class $C^2$ or
embedded of class $W^{2,2}$ bounding a convex domain), the flow converges
smoothly to a round expanding multiply-covered circle.

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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph