# Global Well-Posedness for Eddy-Mean Vorticity Equations on $\mathbb{T}^2$

## TL;DR

This paper proves the global existence and uniqueness of solutions for the two-dimensional vorticity equations on a periodic domain, considering large-scale zonally averaged flows in an incompressible fluid.

## Contribution

It establishes the first rigorous proof of global well-posedness for the eddy-mean vorticity equations on the torus with large-scale zonal flows.

## Key findings

- Global existence and uniqueness of solutions
- Applicable to large-scale zonal flows
- Provides mathematical foundation for 2D vorticity dynamics

## Abstract

We consider the two-dimensional, $\beta$-plane, vorticity equations for an incompressible flow, where the zonally averaged flow varies on scales much larger than the perturbation. We prove global existence and uniqueness of the solution to the equations on periodic settings.