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Finite-time singularities of an aggregation equation in R-n with fractional dissipation
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Li, Dong and Rodrigo, Jose (2009) Finite-time singularities of an aggregation equation in R-n with fractional dissipation. Communications in Mathematical Physics, Vol.287 (No.2). pp. 687-703. doi:10.1007/s00220-008-0669-0
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Official URL: http://dx.doi.org/10.1007/s00220-008-0669-0
Abstract
We consider an aggregation equation in R-n, n >= 2with fractional dissipation, namely, u(t) + del. (u del K * u) = -nu(-Delta)(gamma/2)u, where 0 <= gamma < 1 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e. g. K(x) = e(-|x|). We prove that for a class of smooth initial data, the solutions develop blow-up in finite time.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QC Physics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Communications in Mathematical Physics | ||||
| Publisher: | Springer | ||||
| ISSN: | 0010-3616 | ||||
| Official Date: | April 2009 | ||||
| Dates: |
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| Volume: | Vol.287 | ||||
| Number: | No.2 | ||||
| Number of Pages: | 17 | ||||
| Page Range: | pp. 687-703 | ||||
| DOI: | 10.1007/s00220-008-0669-0 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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