From weakly interacting particles to a regularised Dean–Kawasaki model

Federico Cornalba, Tony Shardlow, Johannes Zimmer

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)
16 Downloads (Pure)


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
Issue number2
Publication statusPublished - 10 Jan 2020


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


Dive into the research topics of 'From weakly interacting particles to a regularised Dean–Kawasaki model'. Together they form a unique fingerprint.

Cite this