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

ISBN-13: 9781470440695

Massimiliano Berti;Riccardo Montalto

Opis

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.

Spis treści

• 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 $\mathcal_{\omega}$
• The Nash-Moser iteration
• Appendix A. Tame estimates for the flow of pseudo-PDEs
• Bibliography.