Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Levy noise

In this article a fractional cross-diffusion system is derived as the rigorous many-particle limit of a multispecies system of moderately interacting particles that is driven by Levy noise. The form of the mutual interaction is motivated by the porous medium equation with fractional potential pressure. Our approach is based on the techniques developed by Oelschlager (1989) and Stevens (2000), in the latter of which the convergence of a regularization of the empirical measure to the solution of a correspondingly regularized macroscopic system is shown. A well-posedness result and the non-negativity of solutions are proved for the regularized macroscopic system, which then yields the same results for the non-regularized fractional cross-diffusion system in the limit. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This article derives a fractional cross-diffusion system as the rigorous limit of a multispecies system of moderately interacting particles driven by Levy noise. The mutual interaction is motivated by the porous medium equation with fractional potential pressure. The approach is based on techniques developed by previous researchers, showing the convergence of a regularization of the empirical measure to the solution of a correspondingly regularized macroscopic system. Well-posedness and non-negativity of solutions are proved for the regularized macroscopic system, yielding the same results for the non-regularized fractional cross-diffusion system in the limit.