Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

José A. Carrillo; Young Pil Choi

doi:10.1007/s00205-021-01676-x

Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

José A. Carrillo, Young Pil Choi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1529-1573
Number of pages	45
Journal	Archive for Rational Mechanics and Analysis
Volume	241
Issue number	3
DOIs	https://doi.org/10.1007/s00205-021-01676-x
Publication status	Published - 2021 Sept

Bibliographical note

Funding Information:
JAC was partially supported by EPSRC Grant Numbers EP/P031587/1 and EP/V051121/1, and the Advanced Grant Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization) of the European Research Council Executive Agency (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 883363). YPC was supported by NRF Grant (No. 2017R1C1B2012918), POSCO Science Fellowship of POSCO TJ Park Foundation, and Yonsei University Research Fund of 2019-22-0212.

Publisher Copyright:
© 2021, The Author(s).

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-021-01676-x

Cite this

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abstract = "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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doi = "10.1007/s00205-021-01676-x",

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AU - Choi, Young Pil

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Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

Abstract

Bibliographical note

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