The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels

Abstract

The authors consider the multidimensional aggregation equation ∂ _t ρ-div(ρ▿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.

Keywords

Well-posedness / Blowup / Osgood condition

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