Fractional Laplacian with singular drift
Volume 207 / 2011
Studia Mathematica 207 (2011), 257-273
MSC: Primary 60J35; Secondary 47A55.
DOI: 10.4064/sm207-3-3
Abstract
For $\alpha \in (1,2)$ we consider the equation $\partial _t u = \varDelta ^{\alpha /2} u + b \cdot \nabla u$, where $b$ is a time-independent, divergence-free singular vector field of the Morrey class $M_1^{1-\alpha }$. We show that if the Morrey norm $\| b\| _{M_1^{1-\alpha }}$ is sufficiently small, then the fundamental solution is globally in time comparable with the density of the isotropic stable process.
