Includes bibliographical references (pages 305-317) and index.
The water waves equations and its asymptotic regimes The Laplace equation The Dirichlet-Neumann operator Well-posedness of the water waves equations Shallow water asymptotics: Systems. Part 1: Derivation Shallow water asymptotics: Systems. Part 2: Justification Shallow water asymptotics: Scalar equations Deep water models and modulation equations 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 Bibliography Index.
(source: Nielsen Book Data)
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. (source: Nielsen Book Data)