Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

José A. Carrillo, Young Pil Choi

Research output: Contribution to journalArticlepeer-review

20 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 languageEnglish
Pages (from-to)1529-1573
Number of pages45
JournalArchive for Rational Mechanics and Analysis
Volume241
Issue number3
DOIs
Publication statusPublished - 2021 Sept

Bibliographical note

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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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