Splash singularity for water waves

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

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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

ASJC Scopus subject areas

  • General


  • Blow-up
  • Euler
  • Free boundary
  • Incompressible


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