A free-boundary problem for Stokes equations: classical solutions

Abstract

The problem considered is that of evolution of the free boundary separating two immiscible viscous fluids with different constant densities. The motion is described by the Stokes equations driven by the gravity force. For flows in a bounded domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 2$, we prove existence and uniqueness of classical solutions, and concentrate on the study of properties of the moving boundary separating the two fluids.