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The Water Waves Problem: Mathematical Analysis and Asymptotics
About this Title
David Lannes, Ecole Normale Supérieure et CNRS, Paris, France
Publication: Mathematical Surveys and Monographs
Publication Year:
2013; Volume 188
ISBNs: 978-0-8218-9470-5 (print); 978-1-4704-0948-7 (online)
DOI: https://doi.org/10.1090/surv/188
MathSciNet review: 3060183
MSC: Primary 35Q53; Secondary 35B25, 35C20, 76B15, 76D33
Table of Contents
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Front/Back Matter
Chapters
- 1. The water waves problem and its asymptotic regimes
- 2. The Laplace equation
- 3. The Dirichlet-Neumann operator
- 4. Well-posedness of the water waves equations
- 5. Shallow water asymptotics: Systems. Part 1: Derivation
- 6. Shallow water asymptotics: Systems. Part 2: Justification
- 7. Shallow water asymptotics: Scalar equations
- 8. Deep water models and modulation equations
- 9. Water waves with surface tension
- Appendix A. More on the Dirichlet-Neumann operator
- Appendix B. Product and commutator estimates
- Appendix C. Asymptotic models: A reader’s digest