Description 
1 online resource (136 pages) 
Series 
Memoirs of the American Mathematical Society Ser. ; v. 256 

Memoirs of the American Mathematical Society Ser

Contents 
Cover; Title page; Chapter 1. Introduction; 1.1. Free boundary Euler equations and water waves; 1.2. The main results; 1.3. Main ideas of the proof; 1.4. Paralinearization and the DirichletNeumann operator; 1.5. Energy estimates and quartic energy inequalities; 1.6. Compatible vectorfield structures; 1.7. Decay and modified scattering; 1.8. Organization; Chapter 2. Preliminaries; 2.1. Notation and basic lemmas; 2.2. The main proposition; Chapter 3. Derivation of the main scalar equation; 3.1. Symmetrization of the equations; 3.2. Higher order derivatives and weights 

Chapter 4. Energy estimates I: high Sobolev estimates4.1. The higher order energy functional; 4.2. Analysis of the symbols and proof of Lemma 4.2; 4.3. Proof of Lemma 4.3; Chapter 5. Energy estimates II: low frequencies; 5.1. The basic low frequency energy; 5.2. The cubic low frequency energy; 5.3. Analysis of the symbols and proof of Lemma 5.2; 5.4. Proof of Lemma 5.3; Chapter 6. Energy estimates III: Weighted estimates for high frequencies; 6.1. The weighted energy functionals; 6.2. Analysis of the symbols and proof of Lemma 6.2; 6.3. Proof of Lemma 6.3 

Chapter 7. Energy estimates IV: Weighted estimates for low frequencies7.1. The cubic low frequency weighted energy; 7.2. Analysis of the symbols and proof of Lemma 7.2; 7.3. Proof of Lemma 7.3; Chapter 8. Decay estimates; 8.1. Set up; 8.2. The "semilinear" normal form transformation; 8.3. The profile; 8.4. The norm and proof of Proposition 8.1; 8.5. The equation for and proof of Proposition 8.5; Chapter 9. Proof of Lemma 8.6; 9.1. Proof of (9.6); 9.2. Proof of (9.7); 9.3. Proof of (9.8); Chapter 10. Modified scattering; Appendix A. Analysis of symbols; A.1. Notation 

A.2. Quadratic symbolsAppendix B. The DirichletNeumann operator; B.1. The perturbed Hilbert transform and proof of Proposition B.1; B.2. Proof of Lemma B.3; Appendix C. Elliptic bounds; C.1. The spaces _{, }; C.2. Linear, quadratic, and cubic bounds; C.3. Semilinear expansions; Bibliography; Back Cover 
Summary 
The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the ""quasilinear Imethod"") which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the socalled ""division problem""). As a result, they are able to consider a suit 
Notes 
Print version record 
Subject 
Waves  Mathematical models


Water waves  Mathematical models


Water waves  Mathematical models


Waves  Mathematical models

Form 
Electronic book

Author 
Pusateri, Fabio

ISBN 
9781470449179 

147044917X 
