Global solutions for the gravity water waves equation in dimension 3

Research output: Contribution to journalArticle

Abstract

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

Original languageEnglish (US)
Pages (from-to)691-754
Number of pages64
JournalAnnals of Mathematics
Volume175
Issue number2
DOIs
StatePublished - Mar 2012

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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