Displaying items by tag: cluster formation
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.
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doi:10.1007/s00028-023-00939-2 |
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Download the Published Version |
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This work is supported by NSF grants DMS #2108264 and DMS #2238219 |
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