Global Regularity for 2D Water Waves with Surface Tension

Download or Read eBook Global Regularity for 2D Water Waves with Surface Tension PDF written by Alexandru D. Ionescu and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle.
Global Regularity for 2D Water Waves with Surface Tension
Author :
Publisher : American Mathematical Soc.
Total Pages : 136
Release :
ISBN-10 : 9781470431037
ISBN-13 : 1470431033
Rating : 4/5 (37 Downloads)

Book Synopsis Global Regularity for 2D Water Waves with Surface Tension by : Alexandru D. Ionescu

Book excerpt: The 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.


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