Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves

Massimiliano Berti, Riccardo Montalto (Autoren)

Buch | Softcover

171 Seiten

2020
American Mathematical Society (Verlag)
978-1-4704-4069-5 (ISBN)

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The 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.

Massimiliano Berti, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy Riccardo Montalto, University of Zurich, Switzerland

Introduction 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.

Erscheinungsdatum	03.03.2020
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	329 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Naturwissenschaften ► Physik / Astronomie
ISBN-10	1-4704-4069-5 / 1470440695
ISBN-13	978-1-4704-4069-5 / 9781470440695
Zustand	Neuware