Long-time dynamics of two-phase flow under gravity

We study the influence of gravity on density-dependent incompressible fluids in a regime where inertial forces are neglected. In particular, we consider piecewise constant densities, leading to the formation of a sharp interface and reducing the evolution to the dynamics of this interface. Depending on the regime and the initial configuration, a rich variety of phenomena arises, including both stable and unstable behaviors. This talk is based on a series of joint works with F. Gancedo, R. Granero, Z. Hu, and Y. Yao.