Fractional Laplacian with singular drift

2011/07/18 by Jakubowski, Tomasz
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1107.3371

Abstract

For α∈ (1,2) we consider the equation ∂_t u = Δ^α/2 u - r b ⋅ ∇ 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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