Regularization for the supercritical quasi-geostrophic equation

TL;DR

This paper proves H"older regularity for weak solutions of the supercritical quasi-geostrophic equation using a De Giorgi type argument, with minimal initial data assumptions.

Contribution

It introduces a novel application of De Giorgi techniques to establish regularity in the supercritical regime with minimal initial data requirements.

Findings

Proved H"older regularity for weak solutions

Applied De Giorgi method in a new context

Reduced initial data assumptions for regularity

Abstract

Motivated by the De Giorgi type argument used in a recent paper by Caffarelli and Vasseur, we prove H\"older-regularity for weak solutions of the supercritical quasi-geostrophic equation with minimal assumptions on the initial datum.