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

2018/11/15 by Cornalba, Federico, Shardlow, Tony, Zimmer, Johannes · 2 citations
#35R60 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.06448

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.

Cited by

• Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality
• Field-Theoretic Simulation of Dean-Kawasaki Dynamics for Interacting Particles

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