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Quasi-periodic standing wave solutions of gravity-capillary water waves /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
[2020]
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1273. |
| Temas: |
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.
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 viscous fluids
> Capillarity (surface tension) [See also 76B45].
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| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 019 | |a 1151184148 | ||
| 020 | |a 9781470456542 |q (electronic bk.) | ||
| 020 | |a 1470456540 |q (electronic bk.) | ||
| 020 | |z 1470440695 |q (print) | ||
| 020 | |z 9781470440695 |q (print) | ||
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| 029 | 1 | |a AU@ |b 000069424757 | |
| 035 | |a (OCoLC)1151271629 |z (OCoLC)1151184148 | ||
| 050 | 4 | |a QC174.26.W28 | |
| 082 | 0 | 4 | |a 530.124 |2 23 |
| 084 | |a 76B15 |a 37K55 |a 76D45 |a 37K50 |a 35S05 |2 msc | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Berti, Massimiliano, |e author. | |
| 245 | 1 | 0 | |a Quasi-periodic standing wave solutions of gravity-capillary water waves / |c Massimiliano Berti, Riccardo Montalto. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c [2020] | |
| 264 | 4 | |c ©2020 | |
| 300 | |a 1 online resource (v, 171 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v number 1273 | |
| 500 | |a "January 2020, volume 263, number 1273 (third of of 7 numbers)." | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Wave equation. | |
| 650 | 0 | |a Differential equations, Partial. | |
| 650 | 6 | |a Équations d'onde. | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 7 | |a Ecuaciones diferenciales |2 embne | |
| 650 | 7 | |a Ecuaciones de onda |2 embne | |
| 650 | 7 | |a Mecánica de fluidos |2 embne | |
| 650 | 7 | |a Differential equations, Partial |2 fast | |
| 650 | 7 | |a Wave equation |2 fast | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Incompressible inviscid fluids |x Water waves, gravity waves; dispersion and scattering, nonlinear interaction. |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] |x Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] |x Perturbations, KAM for inf. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Incompressible viscous fluids |x Capillarity (surface tension) [See also 76B45]. |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] |x Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] |x Bifurcation problems. |2 msc | |
| 650 | 7 | |a Partial differential equations |x Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40] |x Pseudodifferential operators. |2 msc | |
| 700 | 1 | |a Montalto, Riccardo, |e author. | |
| 758 | |i has work: |a Quasi-periodic standing wave solutions of gravity-capillary water waves (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGqYcbXt9JKCJy7Vy9FD7b |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: Berti, Massimiliano. |t Quasi-periodic standing wave solutions of gravity-capillary water waves. |d Providence, RI : American Mathematical Society, 2020 |z 9781470440695 |w (DLC) 2020023139 |w (OCoLC)1132241724 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1273. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6176753 |z Texto completo |
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