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

Eric A. Carlen, Suleyman Ulusoy

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 $n\ge 3$. Like the Patlack-…