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Refined blowup criteria and nonsymmetric blowup of an aggregation equation
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Li, Dong and Rodrigo, Jose (2009) Refined blowup criteria and nonsymmetric blowup of an aggregation equation. Advances in Mathematics, Vol.220 (No.6). pp. 1717-1738. doi:10.1016/j.aim.2008.10.016 ISSN 0001-8708.
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Official URL: http://dx.doi.org/10.1016/j.aim.2008.10.016
Abstract
We consider an aggregation equation in R-d, d >= 2, with fractional dissipation: u(t) +del . (u del K * u) = -nu Lambda(gamma)u, where nu >= 0, 0 < gamma < 1, and K(x) = e(-vertical bar x vertical bar). We prove a refined blowup criteria by which the global existence of solutions is controlled by its L-x(q) norm, for any d/d-1 <= q <= infinity. . We prove the finite time blowup of solutions for a general class of nonsymmetric initial data. The argument presented works for both the inviscid case nu = 0 and the supercritical case nu > 0 and 0 < gamma < 1. Additionally, we present new proofs of blowup which does not use free energy arguments. (C) 2008 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Advances in Mathematics | ||||
| Publisher: | Academic Press | ||||
| ISSN: | 0001-8708 | ||||
| Official Date: | 1 April 2009 | ||||
| Dates: |
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| Volume: | Vol.220 | ||||
| Number: | No.6 | ||||
| Number of Pages: | 22 | ||||
| Page Range: | pp. 1717-1738 | ||||
| DOI: | 10.1016/j.aim.2008.10.016 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | National Science Foundation, Mathematics Department of the University of Iowa, Ministerio de Educacion y Ciencia (Spain) | ||||
| Grant number: | DMS-0635607, MTM2005-05980 |
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