Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with L\'evy-Noise

Viorel Barbu; Michael Röckner

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arXiv · 2210.05612

Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with L\'evy-Noise

Viorel Barbu·Michael Röckner

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Abstract

This work is concerned with the existence of mild solutions to non-linear Fokker-Planck equations with fractional Laplace operator $(-\Delta)^s$ for $s\in\left(\frac12,1\right)$. 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 L\'evy-Noise, as well as the Markov property for their laws are proved.

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Viorel Barbu, Michael Röckner. 2022-10-11. Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with L\'evy-Noise. https://arxiv.org/abs/2210.05612

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