Well-posedness of the free-surface incompressible Euler equations with surface tension


Steve Shkoller
Mathematics
UC Davis

Abstract

I'll describe a new somewhat general methodology for analyzing free boundary problems in (fluid) mechanics, and describe how we can use it to prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with (or without) surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid.