The Cauchy problem on large time for the Water Waves equations with large topography variations

TL;DR

This paper establishes local existence results for water wave equations with significant bottom topography variations, valid over large time scales proportional to 1/epsilon, assuming surface tension effects are present.

Contribution

It provides the first local existence proof for water waves with large bathymetric variations over extended time intervals, incorporating surface tension effects.

Findings

Proves local existence on time scale 1/epsilon

Requires surface tension for the analysis

Handles large bottom topography variations

Abstract

We prove the local existence for the Water Waves equations with large bathymetric variations on a time interval of size 1/\epsilon, where $\epsilon$ measures the amplitude of the wave. We just need the presence of surface tension.