It seems intuitively obvious that a fluid of variable density will eventually rearrange itself over time towards a density profile where the heaviest fluid is at the bottom. However, this phenomenon is difficult to analyze mathematically. The aim of this talk is to present results along these lines for the system coupling the transport equation for density to the Stokes equation for velocity. Perspectives and numerical simulations will also be presented. Joint work with Antoine Leblond and Anne-Laure Dalibard.