Abstract: In this talk, we propose and study a stochastic aggregation-diffusion equation of the Keller-Segel (KS) type for modeling the chemotaxis in dimensions d = 2, 3. Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are discussed. The talk is based on a joint work with Dr. Hui Huang.
Huang, H. and Qiu, J. (2021). The microscopic derivation and well-posedness of the stochastic Keller-Segel equation. J. Nonlinear Sci., 31(1), Paper No. 6.