Dissipation for a non-convex gradient flow problem of a Patlack–Keller–Segel type for densities on [formula omitted], [formula omitted

Abstract

We study an evolution equation that is the gradient flow in the 2-Wasserstein metric of a non-convex functional for densities in Rd with d≥3. Like the Patlack–Keller–Segel system on R2, this evolution equation features a competition between the dispersive effects of diffusion, and the accretive effects of a concentrating drift. We determine a parameter range in which the diffusion dominates, and all mass leaves any fixed compact subset of Rd at an explicit polynomial rate.