From weakly interacting particles to a regularised Dean--Kawasaki model

Federico Cornalba; Tony Shardlow; Johannes Zimmer

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arXiv · 1811.06448

From weakly interacting particles to a regularised Dean--Kawasaki model

Federico Cornalba·Tony Shardlow·Johannes Zimmer

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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.

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Federico Cornalba, Tony Shardlow, Johannes Zimmer. 2018-11-15. From weakly interacting particles to a regularised Dean--Kawasaki model. https://arxiv.org/abs/1811.06448

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