Finite time singularities for water waves with surface tension

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof ar...

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Detalhes bibliográficos
Autores: Castro Martínez, Ángel, Córdoba Gazolaz, Diego, Fefferman, Charles L., Gancedo García, Francisco, Gómez Serrano, Javier
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2012
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/45195
Acesso em linha:http://hdl.handle.net/11441/45195
https://doi.org/10.1063/1.4765339
Access Level:Acceso aberto
Palavra-chave:Euler
Incompressible
Blow-up
Water waves
Splash
Splat
Surface tension
Descrição
Resumo:Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.