Recent progress in the mathematical analysis of active suspensions

This note is based on the recent work [10], which analyzes the collective behaviour of suspensions of self-propelled particles in a fluid flow. The underlying model is a coupled Stokes-kinetic system of PDE's, describing the fluid velocity and the distribution of particles in space and orientation. The stability analysis of the isotropic distribution relies on a careful study of the mixing and enhanced diffusion properties of the system. Mathematically, the interest of this study comes from the orientation variable p∈𝕊 2 , which substitutes to the usual velocity variable v∈ℝ 3 from more standard models, and is responsible for new phenomena and difficulties.