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Splash singularity for water waves.
- Source :
-
Proceedings of the National Academy of Sciences of the United States of America [Proc Natl Acad Sci U S A] 2012 Jan 17; Vol. 109 (3), pp. 733-8. Date of Electronic Publication: 2012 Jan 04. - Publication Year :
- 2012
-
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.
Details
- Language :
- English
- ISSN :
- 1091-6490
- Volume :
- 109
- Issue :
- 3
- Database :
- MEDLINE
- Journal :
- Proceedings of the National Academy of Sciences of the United States of America
- Publication Type :
- Academic Journal
- Accession number :
- 22219372
- Full Text :
- https://doi.org/10.1073/pnas.1115948108