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arXiv · 2310.13463

Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations

Li Chen·Paul Nikolaev·David J. Prömel
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Abstract

The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the nonlinearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean-Vlasov SDEs, which implies propagation of chaos for the interacting particle systems.

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Li Chen, Paul Nikolaev, David J. Prömel. 2023-10-20. Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations. https://arxiv.org/abs/2310.13463

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