Non Linear Singular Drifts and Fractional Operators: when Besov meets Morrey and Campanato

TL;DR

This paper investigates the regularity of solutions to a transport-diffusion equation with nonlinear singular drifts in Morrey-Campanato spaces, highlighting the role of Besov stability in improving regularity results.

Contribution

It introduces a novel analysis of how Besov stability properties influence Hölder regularity for equations with singular drifts, extending previous work in the field.

Findings

Besov stability enhances regularity results for solutions.

More regular drifts diminish the impact of Besov properties.

The study bridges Besov, Morrey, and Campanato space theories.

Abstract

Within the global setting of singular drifts in Morrey-Campanato spaces presented in [6], we study now the H{\"o}lder regularity properties of the solutions of a transport-diffusion equation with nonlinear singular drifts that satisfy a Besov stability property. We will see how this Besov information is relevant and how it allows to improve previous results. Moreover, in some particular cases we show that as the nonlinear drift becomes more regular, in the sense of Morrey-Campanato spaces, the additional Besov stability property will be less useful.