Dissipation for a non-convex gradient flow problem of a Patlack–Keller–Segel type for densities on Rd, d≥3. (July 2021) - Carlen, Eric A.; Ulusoy, Suleyman
Abstract: We study an evolution equation that is the gradient flow in the 2-Wasserstein metric of a non-convex functional for densities in R d with d ≥ 3 . Like the Patlack–Keller–Segel system on R 2, 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 R d at an explicit polynomial rate.