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

2016/06/25 by Aceves-Sanchez, Pedro, Cesbron, Ludovic
#26A33 #35B40 #35Q83 #35Q84 #60J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.07939

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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