Splash singularity for water waves
Analysis of PDEs
2015-05-28 v2
Abstract
We exhibit smooth initial data for the 2D water wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water wave equation that start from a graph, turn over and collapse in a splash singularity (self intersecting curve in one point) in finite time.
Keywords
Cite
@article{arxiv.1106.2120,
title = {Splash singularity for water waves},
author = {Angel Castro and Diego Córdoba and Charles Fefferman and Francisco Gancedo and Javier Gómez-Serrano},
journal= {arXiv preprint arXiv:1106.2120},
year = {2015}
}
Comments
19 pages, 4 figures