Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sticky particle Cucker-Smale dynamics and the entropic selection
  principle for the 1D Euler-alignment system   We develop a global wellposedness theory for weak solutions to the 1D
Euler-alignment system with measure-valued density and bounded velocity. A
satisfactory understanding of the low-regularity theory is an issue of pressing
interest, as smooth solutions may lose regularity in finite time. However, no
such theory currently exists except for a very special class of alignment
interactions. We show that the dynamics of the 1D Euler-alignment system can be
effectively described by a nonlocal scalar balance law, the entropy conditions
of which serves as an entropic selection principle that determines a unique
weak solution of the Euler-alignment system. Moreover, the distinguished weak
solution of the system can be approximated by the sticky particle Cucker-Smale
dynamics. Our approach is largely inspired by the work of Brenier and Grenier
[SIAM J. Numer. Anal, 35(6):2317-2328, 1998] on the pressureless Euler
equations.

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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: physics
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex