The zero surface tension limit of three-dimensional water waves

David M. Ambrose, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review


We establish that the limit of the water wave with surface tension, as surface tension vanishes, is the water wave without surface tension. The main tool is an energy estimate which is uniform in the surface tension parameter. Before es-tablishing estimates, we reformulate the problem using suitable variables and an isothermal parameterization. With these vari-ables and parameterizations, estimates for the water wave with or without surface tension are straightforward. In particular, this provides a new proof of existence of irrotational water waves in three space dimensions.

Original languageEnglish (US)
Pages (from-to)479-521
Number of pages43
JournalIndiana University Mathematics Journal
Issue number2
StatePublished - 2009


  • Surface tension
  • Vortex sheet
  • Water wave
  • Well-posedness

ASJC Scopus subject areas

  • General Mathematics


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