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)|
|Number of pages||6|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Jan 17 2012|
All Science Journal Classification (ASJC) codes
- Free boundary