Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lévy-Noise

Abstract

This work is concerned with the existence of mild solutions to non-linear Fokker-Planck equations with fractional Laplace operator $(-\Delta {)}^s$ for $s\in \left(\frac{1}{2},1\right)$. The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean-Vlasov equations with Lévy-Noise, as well as the Markov property for their laws are proved.