Global existence for capillary water waves

Pierre Germain, Nader Masmoudi, Jalal Shatah

Research output: Contribution to journalArticlepeer-review


Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space-time resonance method and commuting vector fields.

Original languageEnglish (US)
Pages (from-to)625-687
Number of pages63
JournalCommunications on Pure and Applied Mathematics
Issue number4
StatePublished - Apr 1 2015

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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