Chinese Annals of Mathematics, Series B

, Volume 30, Issue 5, pp 463–482

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

Article

DOI: 10.1007/s11401-009-0191-5

Cite this article as:
Bertozzi, A.L. & Laurent, T. Chin. Ann. Math. Ser. B (2009) 30: 463. doi:10.1007/s11401-009-0191-5

Abstract

The authors consider the multidimensional aggregation equation tρ-div(ρK* 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 LpL1, and measure solutions are also considered.

Keywords

Well-posedness Blowup Osgood condition 

2000 MR Subject Classification

35Q80 35Q35 

Copyright information

© Editorial Office of CAM (Fudan University) and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California-Los AngelesLos AngelesUSA