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arXiv · 1606.07939

Fractional diffusion limit for a fractional Vlasov-Fokker-Planck equation

Pedro Aceves-Sanchez·Ludovic Cesbron
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Abstract

This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov-Fokker-Planck equation in which the Laplacian is replaced by a fractional Laplacian. The evolution of the density is governed by a fractional heat equation with the addition of a convective term coming from the external force. The analysis is performed by a modified test function method and by obtaining a priori estimates from quadratic entropy bounds. In addition, we give the proof of existence and uniqueness of solutions to the Vlasov-fractional-Fokker-Planck equation.

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Pedro Aceves-Sanchez, Ludovic Cesbron. 2016-06-25. Fractional diffusion limit for a fractional Vlasov-Fokker-Planck equation. https://arxiv.org/abs/1606.07939

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