Wave breaking in the Whitham equation
Analysis of PDEs
2017-07-10 v3
Abstract
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg-de Vries type for a range of fractional dispersion.
Cite
@article{arxiv.1506.04075,
title = {Wave breaking in the Whitham equation},
author = {Vera Mikyoung Hur},
journal= {arXiv preprint arXiv:1506.04075},
year = {2017}
}