Many Models for Water Waves

TL;DR

This paper reviews various asymptotic models for water waves, especially shallow water and internal waves, extending existing frameworks to include high order and fully dispersive models, providing a comprehensive overview.

Contribution

It offers an extended and detailed overview of water wave models, including new directions like high order and fully dispersive models, beyond previous works.

Findings

Comprehensive overview of shallow water asymptotic models

Extension to high order and fully dispersive models

Discussion of internal and interfacial waves

Abstract

This document is an announcement and preview of a memoir whose full version is available on the Open Math Notes repository of the American Mathematical Society (OMN:202109.111309). In this memoir, I try to provide a fairly comprehensive picture of (mostly shallow water) asymptotic models for water waves. The work and presentation is heavily inspired by the book of D. Lannes, yet extends the discussion into several directions, notably high order and fully dispersive models, and internal/interfacial waves.