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Catalogue Information
Field name	Details
Dewey Class	532.0593
Title	Quasi-periodic standing wave solutions of gravity-capillary water waves (M) / Massimiliano Berti, Riccardo Montalto
Author	Berti, Massimiliano
Added Personal Name	Montalto, Riccardo
Publication	Providence, RI : American Mathematical Society , 2020
Physical Details	v, 171 pages ; 26 cm.
Series	Memoirs of the American Mathematical Society ; 1273
ISBN	9781470440695
Summary Note	We prove the existence and the linear stability of small amplitude time quasiperiodic 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 note	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 Lω -- The Nash-Moser iteration.
Links to Related Works	Subject References: Capillarity . Kolmogorov-Arnold-Moser theory . Standing waves . Water waves--Mathematical models . Wave equation . Authors: Berti, Massimiliano . Montalto, Riccardo . Series: Memoirs of the American Mathematical Society . Classification: 532.0593 . 532.0593 (DDC 23) .

#	Author	Title
1	. Jost, Jürgen 1956- 1	. Nonpositive curvature: geometric and analytic aspects 1
2	. Jost, Jürgen 1956- 2	. Calculus of variations 2
3	. Jost, Jürgen 1956- 3	. Harmonic maps between surfaces: with a special chapter on conformal mappings 3
4		. Geometric analysis and the calculus of variations for Stefan Hildebrandt 4
5	. Jost, Jürgen 1956- 5	. Compact Riemann surfaces: an introduction to contemporary mathematics 5

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