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OverviewThe authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable $x$) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure. Full Product DetailsAuthor: Massimiliano Berti , Riccardo MontaltoPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.329kg ISBN: 9781470440695ISBN 10: 1470440695 Pages: 171 Publication Date: 30 April 2020 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 ContentsIntroduction and main result Functional setting Transversality properties of degenerate KAM theory Nash-Moser theorem and measure estimates Approximate inverse The linearized operator in the normal directions Almost diagonalization and invertibility of $\mathcal{L}_{\omega}$ The Nash-Moser iteration Appendix A. Tame estimates for the flow of pseudo-PDEs Bibliography.ReviewsAuthor InformationMassimiliano Berti, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy Riccardo Montalto, University of Zurich, Switzerland Tab Content 6Author Website:Countries AvailableAll regions |
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