Abstract

The Stokes equations describe the dynamics of a viscous fluid when inertial forces are negligible compared to viscous forces. In this talk, we study the dynamics of two different incompressible Stokes fluids evolving in a horizontally periodic strip. We consider the fluids to have different densities and to be subject to gravity forces. This induces the evolution of the fluids and hence the evolution of the free interface arising between them. There are two differentiated scenarios depending on the regime of the densities: the stable regime (when the denser fluid is below the lighter fluid) and the unstable regime (vice-versa). In both regimes, we study the dynamics of the interface through a contour dynamics approach and we address fundamental questions such as well-posedness, stability and instability of the interface in the stable and unstable regime of the densities.