An application of spectral localization to critical SQG on a ball

TL;DR

This paper investigates the critical surface quasi-geostrophic (SQG) equations within a bounded domain, introducing spectral localization methods to prove existence and uniqueness of solutions in Besov spaces.

Contribution

It develops a spectral localization technique and commutator estimates for the critical SQG equations on a bounded domain, advancing the analytical tools available.

Findings

Existence and uniqueness of strong solutions in Besov spaces

Development of spectral localization technique for SQG

Establishment of commutator estimates

Abstract

We study the Cauchy problem for the quasi-geostrophic equations in a unit ball of the two dimensional space with the homogeneous Dirichlet boundary condition. We show the existence, the uniqueness of the strong solution in the framework of Besov spaces. We establish a spectral localization technique and commutator estimates.