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

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.