On the supercritical fractional diffusion equation with Hardy-type drift

TL;DR

This paper investigates the behavior of the heat kernel in a supercritical fractional diffusion equation with a Hardy-type drift, revealing that certain irregular drifts can cause the heat kernel to vanish at a point for all positive times.

Contribution

It demonstrates that drifts with point irregularities in the critical Hölder space can lead to the heat kernel vanishing at a point, highlighting effects of irregularities in supercritical fractional diffusion.

Findings

Drift irregularities can cause the heat kernel to vanish at a point for all time.

The study characterizes the impact of Hardy-type drifts on the heat kernel behavior.

Irregular drifts in the critical Hölder space significantly influence the solution's properties.

Abstract

We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical H\"{o}lder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all $t>0$.