Global existence for capillary water waves

Research output: Contribution to journalArticle

Abstract

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
Volume68
Issue number4
DOIs
StatePublished - Apr 1 2015

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Energy Estimates
Water waves
Water Waves
Energy Method
Wave equations
Global Existence
Cascade
Wave equation
Vector Field
Space-time
Scattering
Water
Zero

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Global existence for capillary water waves. / Germain, Pierre; Masmoudi, Nader; Shatah, Jalal.

In: Communications on Pure and Applied Mathematics, Vol. 68, No. 4, 01.04.2015, p. 625-687.

Research output: Contribution to journalArticle

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