On the uniqueness of the mild solution of the critical quasi-geostrophic equation

TL;DR

This paper proves the uniqueness of mild solutions for the critical 2D quasi-geostrophic equation in a specific Besov space without requiring additional regularity assumptions.

Contribution

It establishes the uniqueness of solutions in the critical homogeneous Besov space for the first time without extra regularity conditions.

Findings

Uniqueness holds in the space ^0_{\u00000",

No regularity assumptions needed for the proof.

Abstract

We demonstrate that the uniqueness of the mild solution of the two-dimensional quasi-geostrophic equation with the critical dissipation holds in the scaling critical homogeneous Besov space $\dot{B}^0_{\infty,1}$. We consider a solustion of integral equation, and our result does not need regularity assumption.