Refined blowup criteria and nonsymmetric blowup of an aggregation equation
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. ISSN 0001-8708Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.aim.2008.10.016
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 > Mathematics|
|Journal or Publication Title:||Advances in Mathematics|
|Official Date:||1 April 2009|
|Number of Pages:||22|
|Page Range:||pp. 1717-1738|
|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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