Two-component equations modelling water waves with constant vorticity

TL;DR

This paper derives a two-component nonlinear system modeling shallow water waves with constant vorticity, proves its well-posedness using geometric methods, and establishes criteria for global existence of solutions.

Contribution

It introduces a novel two-component model for water waves with vorticity and applies geometric analysis to prove well-posedness and global existence criteria.

Findings

Established well-posedness of the model

Recast the equations as a geodesic flow

Provided criteria for global solutions

Abstract

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite dimensional manifold. Finally, we provide a criteria for global existence.