Global solutions of quasi-geostrophic shallow-water fronts

TL;DR

This paper studies the global behavior of solutions to a nonlinear, nonlocal dispersive equation modeling quasi-geostrophic shallow-water fronts, proving existence results for initial data near flat fronts.

Contribution

It derives the contour dynamics equation for QGSW fronts and establishes global existence of solutions close to flat fronts.

Findings

Derived the contour dynamics equation for QGSW fronts

Proved global existence of solutions near flat fronts

Established mathematical framework for QGSW front analysis

Abstract

In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW front, which is a nonlinear, nonlocal dispersive equation, and prove the global existence of the solutions when the initial data is sufficiently close to a flat front.