Finite-Time Blow-Up of Solutions of an Aggregation Equation

Thomas Laurent
UCLA
laurent@math.ucla.edu

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.