Well-posedness of the free-surface incompressible Euler equations with or without surface tension
Analysis of PDEs
2007-05-23 v3 Mathematical Physics
math.MP
Abstract
We provide a new method for treating free boundary problems in perfect fluids, and 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. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.
Cite
@article{arxiv.math/0511236,
title = {Well-posedness of the free-surface incompressible Euler equations with or without surface tension},
author = {Daniel Coutand and Steve Shkoller},
journal= {arXiv preprint arXiv:math/0511236},
year = {2007}
}
Comments
To appear in J. Amer. Math. Soc., 96 pages