On the splash singularity for the free-surface of a Navier–Stokes fluid

Daniel Coutand, Steve Shkoller

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
83 Downloads (Pure)


In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for d-dimensional flows, or 3, the free-surface of a viscous water wave, modeled by the incompressible Navier–Stokes equations with moving free-boundary, has a finite-time splash singularity for a large class of specially prepared initial data. In particular, we prove that given a sufficiently smooth initial boundary (which is close to self-intersection) and a divergence-free velocity field designed to push the boundary towards self-intersection, the interface will indeed self-intersect in finite time.
Original languageEnglish
Pages (from-to)475-503
Number of pages29
JournalAnnales de l'Institut Henri Poincaré (C) Analyse Non Linéaire
Issue number2
Early online date17 Jul 2018
Publication statusPublished - Apr 2019


  • Navier–Stokes
  • Free-boundary problem
  • Finite-time singularity
  • Splash singularity
  • Interface singularity

ASJC Scopus subject areas

  • General Mathematics


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