Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space

TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 2D quasi-geostrophic equation with large initial data in a critical Besov space, advancing understanding of its well-posedness.

Contribution

It establishes the global well-posedness of the 2D quasi-geostrophic equation in a critical Besov space for large initial data, which was previously unresolved.

Findings

Global and unique strong solutions exist for large data

Solutions are valid in the critical Besov space $ ext{dot}B^{2-2eta}_{2, ext{infty}}$

The result applies to initial data in a scale-invariant space

Abstract

We show that the the 2 D quasi-geostrophic equation has global and unique strong solution, when the (large) data belongs in the critical, scale invariant space $\dot{B}^{2-2\al}_{2, \infty}\cap L^{2/(2\al-1)}$.