A Priori Estimates for Two-Dimensional Water Waves with Angled Crests

@article{Kinsey2014APE,
title={A Priori Estimates for Two-Dimensional Water Waves with Angled Crests},
author={R. H. Kinsey and S. Wu},
journal={arXiv: Analysis of PDEs},
year={2014}
}

We consider the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly non-right angle; and where the free interface can be non-$C^1$ with angled crests. We assume that the air has density zero, the fluid is inviscid, incompressible, irrotational, and subject to the gravitational force, and the surface tension is zero. In this regime, only a degenerate Taylor stability criterion $-\frac{\partial P}{\partial \bf {n}} \ge 0$ holds… Expand