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Friday, 28 July 2023 09:48

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

 

Trevor M. Leslie and Changhui Tan


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.


 This work is supported by NSF grants DMS #2108264 and DMS #2238219

arXiv Preprint 2307.13626.

Read 160 times Last modified on Friday, 28 July 2023 10:03