From weakly interacting particles to a regularised Dean–Kawasaki model

Federico Cornalba, Tony Shardlow, Johannes Zimmer

Research output: Contribution to journalArticle

Abstract

The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean-Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean-Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.

Original languageEnglish
Pages (from-to)864-891
Number of pages28
JournalNonlinearity
Volume33
Issue number2
DOIs
Publication statusPublished - 10 Jan 2020

Keywords

  • math.PR
  • math.AP
  • 60H15 (35R60)

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