Global solutions for the gravity water waves system in 2d

Alexandru D. Ionescu, Fabio Pusateri

Research output: Contribution to journalArticle

67 Scopus citations

Abstract

We consider the gravity water waves system in the case of a one dimensional interface, for sufficiently smooth and localized initial data, and prove global existence of small solutions. This improves the almost global existence result of Wu (Invent Math 177(1):45–135, 2009). We also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear, unlike the three dimensional case (Germain et al., Ann Math 175(2):691–754, 2012; Wu, Invent Math 184(1):125–220, 2011). In particular, we identify a suitable nonlinear logarithmic correction and show modified scattering. The solutions we construct in this paper appear to be the first global smooth nontrivial solutions of the gravity water waves system in 2D.

Original languageEnglish (US)
Pages (from-to)653-804
Number of pages152
JournalInventiones Mathematicae
Volume199
Issue number3
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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