Global solutions for the gravity water waves equation in dimension 3

P. Germain, Nader Masmoudi, Jalal Shatah

Research output: Contribution to journalArticlepeer-review

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 L2 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. To cite this article: P. Germain et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Original languageEnglish (US)
Pages (from-to)897-902
Number of pages6
JournalComptes Rendus Mathematique
Volume347
Issue number15-16
DOIs
StatePublished - Aug 2009

ASJC Scopus subject areas

  • Mathematics(all)

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