# Global well-posedness of critical surface quasigeostrophic equation on the sphere

## TL;DR

This paper proves the global well-posedness of the critical surface quasigeostrophic equation on a sphere, extending previous Euclidean results by improving fractional Laplacian inequalities.

## Contribution

It introduces a new approach to establish well-posedness on the sphere by enhancing fractional Laplacian inequalities, building on prior Euclidean analyses.

## Key findings

- Established global well-posedness on the sphere
- Improved pointwise inequalities for fractional Laplacians
- Extended Euclidean results to spherical geometry

## Abstract

In this paper we prove global well-posedness of the critical surface quasigeostrophic equation on the two dimensional sphere building on some earlier work of the authors. The proof relies on an improving of the previously known pointwise inequality for fractional laplacians as in the work of Constantin and Vicol for the euclidean setting.