On the three-dimensional Euler equations with a free boundary subject to surface tension (Q2581837)

The paper deals with an incompressible ideal fluid with a free surface subject to surface tension. A priori estimates for solutions are obtained. The bounds are established by combining estimates of energy type with estimates of vorticity type and rely on a study of the regularity properties of the pressure function. An suitable artificial coordinate system is used instead of the Lagrangian coordinates. A local existence theorem is proved in the case when the vorticity vanishes on the boundary initially (and, therefore, for all times). A solution to the Euler equations is obtained as a vanishing viscosity limit of solutions to appropriate Navier-Stokes systems.