UCLA

**Abstract**: The aggregation equation
arises in a number of contexts of recent interest in the physics and
biology literature. Depending on how regular the potential is, we prove
either local or global existence for the solutions. For example, we will see
that for
we have local existence whereas for
we have global existence. For potential with a Lipschitz
point at the origin, e.g.
, we prove finite-time blow-up of
solutions from specific smooth initial data.