Global regularity for 2d water waves with surface tension

Alexandru D. Ionescu, Fabio Giuseppe Pusateri

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method, based on energy estimates and dispersive analysis, which allows us to deal simultaneously with strong singularities arising from time resonances in the applications of the normal form method and with nonlinear scattering. As a result, we are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.

Original languageEnglish (US)
Pages (from-to)1-136
Number of pages136
JournalMemoirs of the American Mathematical Society
Volume256
Issue number1227
DOIs
StatePublished - Nov 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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