Stratified Steady Periodic Water Waves

TL;DR

This paper proves the existence of a broad class of two-dimensional stratified water waves that are periodic, traveling, and can have large variations in density, speed, and amplitude, under gravity over a flat bed.

Contribution

It establishes the existence of a global continuum of classical solutions for stratified water waves with large density variations and amplitudes.

Findings

Existence of a global continuum of solutions

Waves can have large density variations

Waves can exhibit large speed and amplitude

Abstract

This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic and traveling. These waves, moreover, can exhibit large density variation, speed and amplitude.