Global regularity for 2D water waves with surface tension /
"We consider the full irrotatioal 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 t...
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society,
[2018]
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| Series: | Memoirs of the American Mathematical Society ;
no. 1227 Memoirs of the American Mathematical Society no. 1227 |
| Subjects: | |
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| Summary: | "We consider the full irrotatioal 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."--Page v |
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| Item Description: | "November 2018, volume 256, number 1227 (third of 6 numbers)." |
| Physical Description: | v, 123 pages ; 26 cm |
| Bibliography: | Includes bibliographical references (pages 121-123) Includes bibliographical references |
| ISBN: | 1470431033 9781470431037 |
| ISSN: | 0065-9266 ; |