The derivation of swarming models: Mean-field limit and Wasserstein distances

José Antonio Carrillo; Young Pil Choi; Maxime Hauray

doi:10.1007/978-3-7091-1785-9_1

The derivation of swarming models: Mean-field limit and Wasserstein distances

José Antonio Carrillo, Young Pil Choi, Maxime Hauray

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

119 Citations (Scopus)

Abstract

These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order models for swarming. We focus on the question of passing from the discrete to the continuum model in the Dobrushin framework. We show how to use related techniques from fluid mechanics equations applied to first order models for swarming, also called the aggregation equation. We give qualitative bounds on the approximation of initial data by particles to obtain the mean-field limit for radial singular (at the origin) potentials up to the Newtonian singularity. We also show the propagation of chaos for more restricted set of singular potentials.

Original language	English
Title of host publication	CISM International Centre for Mechanical Sciences, Courses and Lectures
Publisher	Springer International Publishing
Pages	1-46
Number of pages	46
DOIs	https://doi.org/10.1007/978-3-7091-1785-9_1
Publication status	Published - 2014

Publication series

Name	CISM International Centre for Mechanical Sciences, Courses and Lectures
Volume	553
ISSN (Print)	0254-1971
ISSN (Electronic)	2309-3706

Bibliographical note

Funding Information:
JAC was partially supported by the project MTM2011-27739-C04-02 DGI (Spain) and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. JAC acknowledges support from the Royal Society by a Wolfson Research Merit Award. YPC was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (ref. 2012R1A6A3A03039496). JAC and YPC were supported by Engineering and Physical Sciences Research Council grants with references EP/K008404/1 (individual grant) and EP/I019111/1 (platform grant).

Publisher Copyright:
© 2014, CISM, Udine.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Mechanics of Materials
Mechanical Engineering
Computer Science Applications

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10.1007/978-3-7091-1785-9_1

Cite this

Carrillo, J. A., Choi, Y. P., & Hauray, M. (2014). The derivation of swarming models: Mean-field limit and Wasserstein distances. In CISM International Centre for Mechanical Sciences, Courses and Lectures (pp. 1-46). (CISM International Centre for Mechanical Sciences, Courses and Lectures; Vol. 553). Springer International Publishing. https://doi.org/10.1007/978-3-7091-1785-9_1

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author = "Carrillo, {Jos{\'e} Antonio} and Choi, {Young Pil} and Maxime Hauray",

note = "Funding Information: JAC was partially supported by the project MTM2011-27739-C04-02 DGI (Spain) and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. JAC acknowledges support from the Royal Society by a Wolfson Research Merit Award. YPC was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (ref. 2012R1A6A3A03039496). JAC and YPC were supported by Engineering and Physical Sciences Research Council grants with references EP/K008404/1 (individual grant) and EP/I019111/1 (platform grant). Publisher Copyright: {\textcopyright} 2014, CISM, Udine.",

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The derivation of swarming models: Mean-field limit and Wasserstein distances. / Carrillo, José Antonio; Choi, Young Pil; Hauray, Maxime.
CISM International Centre for Mechanical Sciences, Courses and Lectures. Springer International Publishing, 2014. p. 1-46 (CISM International Centre for Mechanical Sciences, Courses and Lectures; Vol. 553).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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The derivation of swarming models: Mean-field limit and Wasserstein distances

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