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 nonlinear 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.