Fractional Laplacian with singular drift

Details Fractional Laplacian with singular drift Fractional Laplacian with singular drift

2011-07-18

arxiv.org/abs/1107.3371v1

Mathematics

Probability

Scientific paper

For $\alpha \in (1,2)$ we consider the equation $\partial_t u =
\Delta^{\alpha/2} u - r b \cdot \nabla u$, where $b$ is a divergence free
singular vector field not necessarily belonging to the Kato class. We show that
for sufficiently small $r>0$ the fundamental solution is globally in time
comparable with the density of the isotropic stable process

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