Finite-time blow-up of L∞-weak solutions of an aggregation equation

We consider the aggregation equation utWe assume that K is rotationally invariant, nonnegative, decaying at infinity, with at worst a Lipschitz point at the origin.We prove existence, uniqueness, and continuation of solutions.Finite time blow-up (in the L ∞ norm) of solutions is proved when the kernel has precisely a Lipschitz point at the origin.