Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global regularity for the fractional Euler alignment system   We study a pressureless Euler system with a nonlinear density-dependent
alignment term, originating in the Cucker-Smale swarming models. The alignment
term is dissipative in the sense that it tends to equilibrate the velocities.
Its density dependence is natural: the alignment rate increases in the areas of
high density due to species discomfort. The diffusive term has the order of a
fractional Laplacian $(-\partial_{xx})^{\alpha/2}$, $\alpha \in (0, 1)$. The
corresponding Burgers equation with a linear dissipation of this type develops
shocks in a finite time. We show that the alignment nonlinearity enhances the
dissipation, and the solutions are globally regular for all $\alpha \in (0,
1)$. To the best of our knowledge, this is the first example of such
regularization due to the non-local nonlinear modulation of dissipation.

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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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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: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con