Vol. 9, No. 4, 2021

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Mean-field limit for particle systems with topological interactions

Dario Benedetto, Emanuele Caglioti and Stefano Rossi

Vol. 9 (2021), No. 4, 423–440
DOI: 10.2140/memocs.2021.9.423
Abstract

The mean-field limit for systems of self-propelled agents with “topological interaction” cannot be obtained by means of the usual Dobrushin approach. We get results by adapting to the multidimensional case the techniques developed by Trocheris in 1986 to treat the Vlasov–Poisson equation in one dimension.

Keywords
mean-field limit, topological interaction, Cucker–Smale model
Mathematical Subject Classification
Primary: 35Q83, 35Q92, 82C40
Milestones
Received: 15 October 2021
Revised: 26 October 2021
Accepted: 29 November 2021
Published: 14 March 2022

Communicated by Mario Pulvirenti
Authors
Dario Benedetto
Dipartimento di Matematica
Università di Roma “La Sapienza”
Roma
Italy
Emanuele Caglioti
Dipartimento di Matematica
Università di Roma “La Sapienza”
Roma
Italy
Stefano Rossi
Dipartimento di Matematica
Università di Roma “La Sapienza”
Roma
Italy