From weakly interacting particles to a regularised Dean-Kawasaki model

F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.


Journal Article | Published | English
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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.
Publishing Year
Date Published
2020-01-10
Journal Title
Nonlinearity
Volume
33
Issue
2
Page
864-891
ISSN
eISSN
IST-REx-ID

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Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174
Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity, 33(2), 864–891. https://doi.org/10.1088/1361-6544/ab5174
Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity 33, no. 2 (2020): 864–91. https://doi.org/10.1088/1361-6544/ab5174.
F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2, pp. 864–891, 2020.
Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.
Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:10.1088/1361-6544/ab5174.

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