摘要
The authors consider the multidimensional aggregation equation tp-div(p K* ρ) = 0 in which the radially symmetric attractive interaction kernel has a mild singularity at the origin (Lipschitz or better), and review recent results on this problem concerning well-posedness of nonnegative solutions and finite time blowup in multiple space dimensions depending on the behavior of the kernel at the origin. The problem with bounded initial data, data in L^p ∩ L^1, and measure solutions are also considered.
基金
Project supported by the Office of Naval Research,the Army Research Office and the National Science Foundation (No.DMS-0907931)