|Dept.||Institut de Mathématiques de Bordeaux|
In this talk, I will give an overview of some recent results on the so-called transport-Stokes system which describes sedimentation of inertialess particles in a viscous flow. This system couples a transport equation and the steady Stokes equations in the full 3D space. I will address the Cauchy problem, the regularity of the particle trajectories and the controllability issue. We will see that the system has some similarity to the incompressible Euler system. Some of the exposed results have been obtained in collaboration with Amina Mecherbet.