Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulate...

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Detalles Bibliográficos
Autores principales: Carrillo, José A., Choi, Young-Pil
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550335/
https://www.ncbi.nlm.nih.gov/pubmed/34720114
http://dx.doi.org/10.1007/s00205-021-01676-x
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author Carrillo, José A.
Choi, Young-Pil
author_facet Carrillo, José A.
Choi, Young-Pil
author_sort Carrillo, José A.
collection PubMed
description We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.
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spelling pubmed-85503352021-10-29 Mean-Field Limits: From Particle Descriptions to Macroscopic Equations Carrillo, José A. Choi, Young-Pil Arch Ration Mech Anal Article We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions. Springer Berlin Heidelberg 2021-06-01 2021 /pmc/articles/PMC8550335/ /pubmed/34720114 http://dx.doi.org/10.1007/s00205-021-01676-x Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Carrillo, José A.
Choi, Young-Pil
Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title_full Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title_fullStr Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title_full_unstemmed Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title_short Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
title_sort mean-field limits: from particle descriptions to macroscopic equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550335/
https://www.ncbi.nlm.nih.gov/pubmed/34720114
http://dx.doi.org/10.1007/s00205-021-01676-x
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