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Author Berti, Massimiliano, author.

Title Quasi-periodic standing wave solutions of gravity-capillary water waves / Massimiliano Berti, Riccardo Montalto
Published Providence, RI : American Mathematical Society, [2020]
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Description 1 online resource (v, 171 pages)
Series Memoirs of the American Mathematical Society ; number 1273
Memoirs of the American Mathematical Society ; no. 1273
Contents Cover -- Title page -- Chapter 1. Introduction and main result -- 1.1. Ideas of proof -- 1.2. Notation -- Chapter 2. Functional setting -- 2.1. Pseudo-differential operators and norms -- 2.2. ̂{ ₀}-tame and ̂{ ₀}-modulo-tame operators -- 2.3. Integral operators and Hilbert transform -- 2.4. Dirichlet-Neumann operator -- Chapter 3. Transversality properties of degenerate KAM theory -- Chapter 4. Nash-Moser theorem and measure estimates -- 4.1. Nash-Moser Théoréme de conjugaison hypothétique -- 4.2. Measure estimates -- Chapter 5. Approximate inverse -- 5.1. Estimates on the perturbation
5.2. Almost approximate inverse -- Chapter 6. The linearized operator in the normal directions -- 6.1. Linearized good unknown of Alinhac -- 6.2. Symmetrization and space reduction of the highest order -- 6.3. Complex variables -- 6.4. Time-reduction of the highest order -- 6.5. Block-decoupling up to smoothing remainders -- 6.6. Elimination of order \paₓ: Egorov method -- 6.7. Space reduction of the order ̂{1/2} -- 6.8. Conclusion: partial reduction of ℒ_{\om} -- Chapter 7. Almost diagonalization and invertibility of ℒ_{\om} -- 7.1. Proof of Theorem 7.3
7.2. Almost-invertibility of ℒ_{\om} -- Chapter 8. The Nash-Moser iteration -- 8.1. Proof of Theorem 4.1 -- Appendix A. Tame estimates for the flow of pseudo-PDEs -- Bibliography -- Back Cover
Summary 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
Notes "January 2020, volume 263, number 1273 (third of of 7 numbers)."
Bibliography Includes bibliographical references
Subject Differential equations, Partial.
Wave equation.
Differential equations, Partial
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] -- Bifurcation problems.
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] -- Perturbations, KAM for inf.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Incompressible inviscid fluids -- Water waves, gravity waves; dispersion and scattering, nonlinear interaction.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Incompressible viscous fluids -- Capillarity (surface tension) [See also 76B45].
Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40] -- Pseudodifferential operators.
Wave equation
Form Electronic book
Author Montalto, Riccardo, author.
ISBN 1470456540
9781470456542