On the global well-posedness of the critical quasi-geostrophic equation

TL;DR

This paper proves the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data in a specific critical Besov space, advancing understanding of its mathematical behavior.

Contribution

It establishes the global existence and uniqueness of solutions for large initial data in the critical Besov space, a significant extension beyond small data results.

Findings

Global well-posedness for large initial data

Solutions exist and are unique in the critical Besov space

Advances understanding of the equation's mathematical properties

Abstract

We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space $\dot B^0_{\infty,1}(\RR^2).$