Displaying items by tag: cluster formation

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