Refined blowup criteria and nonsymmetric blowup of an aggregation equation

摘要

We consider an aggregation equation in R~d, d≥2, with fractional dissipation: u_t +V _ (u_÷K * u) = _v ~r u, where v≥0, 00 and 0<γ<1. Additionally, we present new proofs of blowup which does not use free energy arguments.