Analysis of a fractional cross-diffusion system for multi-species populations

Abstract: The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance interactions; they have been derived in the many-particle limit from moderately interacting particle systems with L\'evy noise. The existence proof is based on a three-level approximation scheme, entropy and moment estimates, and a new Aubin-Lions compactness lemma in the whole space.