Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

We rigorously justify in 3 D the main asymptotic models used in coastal oceanography,
including: shallow-water equations, Boussinesq systems, Kadomtsev–Petviashvili (KP) …

Derived here in a systematic way, and for a large class of scaling regimes are asymptotic
models for the propagation of internal waves at the interface between two layers of …

In this paper, we describe a numerical method to solve numerically the weakly dispersive
fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based …

In this paper, we derive a new formulation of the water waves equations with vorticity that
generalizes the well-known Zakharov-Craig-Sulem formulation used in the irrotational case …

We consider in this paper the well-posedness on time intervals of order 1/ϵ for the Cauchy
problem associated to two-dimensional dispersive systems of Boussinesq type which model …

The present book is entirely devoted to the development of mathematical models and
numerical algorithms to simulate the generation and propagation of long surface water …

Considered here are Boussinesq systems of equations of surface water wave theory over a
variable bottom. A simplified such Boussinesq system is derived and solved numerically by …

This paper is a continuation of a previous work by two of the authors [J.-C. Saut and Li Xu, J.
Math. Pures Appl.(9), 97 (2012), pp. 635--662.] on long time existence for Boussinesq …

In this paper we deal with the long time existence issue for the Cauchy problem associated
to some asymptotic models for long wave, small amplitude gravity surface water waves. We …