Global mild solutions for a transport-diffusion equation with a rough drift

TL;DR

This paper constructs global mild solutions for a class of transport-diffusion equations with rough drift terms involving Calderón-Zygmund operators, advancing understanding in critical settings.

Contribution

It introduces a method to establish global solutions in critical regimes for equations with rough drifts involving Calderón-Zygmund operators.

Findings

Successfully constructed global mild solutions in a critical setting.

Extended the theory to include rough Calderón-Zygmund operator drifts.

Provided a framework for analyzing transport-diffusion equations with irregular drifts.

Abstract

We construct here global mild solutions in a critical setting for a class of transport-diffusion equations with a drift term that involves rough Calder{\'o}n-Zygmund operators.