We will consider the initial value problem for the motion of incompressible inviscid fluids with free boundary and surface tension on the boundary. We will show how to find solutions. We also show that If the initial boundary has constant mean curvature, then the motion converges to motion of a fluid with fixed boundary as the surface tension constant gets large.
We shall also show that the absence of surface tension can lead to an ill-posed problem.
The initial value problem for fluids with free boundary and surface tension Sponsored by the Meyer Fund