The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels
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- Bertozzi, A.L. & Laurent, T. Chin. Ann. Math. Ser. B (2009) 30: 463. doi:10.1007/s11401-009-0191-5
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The authors consider the multidimensional aggregation equation ∂tρ-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 Lp ∩ L1, and measure solutions are also considered.