Splash singularity for water waves

Angel Castro, Diego Córdoba, Charles L. Fefferman, Francisco Gancedo, Javier Gómez-Serrano

Research output: Contribution to journalArticle

23 Scopus citations

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 languageEnglish (US)
Pages (from-to)733-738
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume109
Issue number3
DOIs
StatePublished - Jan 17 2012

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Blow-up
  • Euler
  • Free boundary
  • Incompressible

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