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OverviewThe authors 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 the authors' analysis is to develop a sufficiently robust method (the ``quasilinear I-method'') which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called ``division problem''). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' 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. Full Product DetailsAuthor: Alexandru D. Ionescu , Fabio PusateriPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.205kg ISBN: 9781470431037ISBN 10: 1470431033 Pages: 119 Publication Date: 30 May 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationAlexandru D. Ionescu, Princeton University, NJ. Fabio Pusateri, Princeton University, NJ. Tab Content 6Author Website:Countries AvailableAll regions |