Abstract
We exhibit smooth initial data for the two-dimensional (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.
Original language | English (US) |
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Pages (from-to) | 733-738 |
Number of pages | 6 |
Journal | Proceedings of the National Academy of Sciences of the United States of America |
Volume | 109 |
Issue number | 3 |
DOIs | |
State | Published - Jan 17 2012 |
All Science Journal Classification (ASJC) codes
- General
Keywords
- Blow-up
- Euler
- Free boundary
- Incompressible