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Full Description
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.
Contents
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.
