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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

Journal of Evolution Equations, Volume 24, Article 8, 45pp. (2024).


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.


   doi:10.1007/s00028-023-00939-2
 Download the Published Version
 This work is supported by NSF grants DMS #2108264 and DMS #2238219
Read 563 times Last modified on Monday, 12 February 2024 10:19