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arXiv · 2307.13626

Finite- and Infinite-Time Cluster Formation for Alignment Dynamics on the Real Line

Trevor M. Leslie·Changhui Tan
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Abstract

We show that the locations where finite- and infinite-time clustering occurs for the 1D Euler-alignment system can be determined using only the initial data. Our present work provides the first results on the structure of the finite-time singularity set and asymptotic clusters associated to a weak solution. In many cases, the eventual size of the cluster can be read off directly from the flux associated to a scalar balance law formulation of the system.

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Trevor M. Leslie, Changhui Tan. 2023-07-25. Finite- and Infinite-Time Cluster Formation for Alignment Dynamics on the Real Line. https://arxiv.org/abs/2307.13626

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