From a multiscale derivation of nonlinear cross-diffusion models to Keller-Segel models in a Navier-Stokes fluid

This paper deals with a micro-macro derivation of a variety of cross-diffusion models for a large system of active particles. Some of the models at the macroscopic scale can be viewed as developments of the classical Keller-Segel model. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. The second part is devoted to the design of the micro-macro general framework, where methods of the kinetic theory are used to model the dynamics of the system including the case of coupling with a fluid. The third part deals with the derivation of macroscopic models from the underlying description, delivered within a general framework of the kinetic theory.