Consistency analysis for combined homogenization and shallow water limit of water waves

TL;DR

This paper extends the analysis of water wave models by relaxing periodicity assumptions, allowing for more general topographies in homogenization and shallow water limit studies.

Contribution

It introduces a framework that handles non-periodic topographies in water wave models, broadening the applicability of homogenization techniques.

Findings

Relaxed periodicity condition in water wave homogenization.

Established consistency results for general topographies.

Broadened the theoretical understanding of water wave limits.

Abstract

We consider a shallow water model in a homogenization framework. For periodic topographies, Craig, Lannes and Sulem have established a consistency result under some non-resonance conditions. In the present contribution, we significantly relax the periodicity condition and treat general topographies under minimal assumptions.