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We study an evolution equation that is the gradient flow in the$2$-Wasserstien metric of a non-convex functional for densities in$\mathbb{R}^n$ with $n \geq 3$. Like the Patlack-Keller-Segel system on$\mathbb{R}^2$, this evolution equation features a competition between thedispersive effects of diffusion, and the accretive effects of a concentratingdrift. We determine a parameter range in which the diffusion dominates, and allmass leaves any fixed compact subset of $\mathbb{R}^n$ at an explicitpolynomial rate.

Dissipation for a non-convex gradient flow problem of a Patlack-Keller-Segel type for densities on $\mathbb{R}^n$, $n\geq 3$