Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

José A. Carrillo, Young Pil Choi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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 languageEnglish
Pages (from-to)1529-1573
Number of pages45
JournalArchive for Rational Mechanics and Analysis
Issue number3
Publication statusPublished - 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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