The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki type equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean-Kawasaki type model based on second order Langevin dynamics by analysing a system of weakly interacting particles. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise regime stochastic perturbation of the undamped McKean-Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.
- 60H15 (35R60)