Splash singularity for water waves

We exhibit smooth initial data for the two-dimensional (2D) waterwave 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 fro...

Descripción completa

Detalles Bibliográficos
Autores: Castro Martínez, Ángel, Córdoba Gazolaz, Diego, Fefferman, Charles L., Gancedo García, Francisco, Gómez Serrano, Javier
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/45166
Acceso en línea:http://hdl.handle.net/11441/45166
https://doi.org/10.1073/pnas.1115948108
Access Level:acceso abierto
Palabra clave:Blow-up
Euler
Incompressible
Free boundary
Descripción
Sumario:We exhibit smooth initial data for the two-dimensional (2D) waterwave 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.