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The Water Waves Problem: Mathematical Analysis and Asymptotics
 
David Lannes Ecole Normale Supérieure et CNRS, Paris, France
Front Cover for The Water Waves Problem
Available Formats:
Hardcover ISBN: 978-0-8218-9470-5
Product Code: SURV/188
List Price: $104.00
MAA Member Price: $93.60
AMS Member Price: $83.20
Electronic ISBN: 978-1-4704-0948-7
Product Code: SURV/188.E
List Price: $98.00
MAA Member Price: $88.20
AMS Member Price: $78.40
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $156.00
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AMS Member Price: $124.80
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The Water Waves Problem: Mathematical Analysis and Asymptotics
David Lannes Ecole Normale Supérieure et CNRS, Paris, France
Available Formats:
Hardcover ISBN:  978-0-8218-9470-5
Product Code:  SURV/188
List Price: $104.00
MAA Member Price: $93.60
AMS Member Price: $83.20
Electronic ISBN:  978-1-4704-0948-7
Product Code:  SURV/188.E
List Price: $98.00
MAA Member Price: $88.20
AMS Member Price: $78.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $156.00
MAA Member Price: $140.40
AMS Member Price: $124.80
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1882013; 321 pp
    MSC: Primary 76; 35;

    This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models. Which model provides the best description of waves such as tsunamis or tidal waves? How can water waves equations be transformed into simpler asymptotic models for applications in, for example, coastal oceanography? This book proposes a simple and robust framework for studying these questions.

    The book should be of interest to graduate students and researchers looking for an introduction to water waves equations or for simple asymptotic models to describe the propagation of waves. Researchers working on the mathematical analysis of nonlinear dispersive equations may also find inspiration in the many (and sometimes new) models derived here, as well as precise information on their physical relevance.

    Readership

    Graduate students and research mathematicians interested in nonlinear PDEs and applications to oceanography.

  • Table of Contents
     
     
    • 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
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Volume: 1882013; 321 pp
MSC: Primary 76; 35;

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models. Which model provides the best description of waves such as tsunamis or tidal waves? How can water waves equations be transformed into simpler asymptotic models for applications in, for example, coastal oceanography? This book proposes a simple and robust framework for studying these questions.

The book should be of interest to graduate students and researchers looking for an introduction to water waves equations or for simple asymptotic models to describe the propagation of waves. Researchers working on the mathematical analysis of nonlinear dispersive equations may also find inspiration in the many (and sometimes new) models derived here, as well as precise information on their physical relevance.

Readership

Graduate students and research mathematicians interested in nonlinear PDEs and applications to oceanography.

  • 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
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