Li, Dong and Rodrigo, Jose L. (2010) Wellposedness and regularity of solutions of an aggregation equation. Revista Matematica Iberoamericana, Vol.26 (No.1). pp. 261-294. ISSN 0213-2230.

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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 >= 2 and K(x) = e(-vertical bar x vertical bar) In the supercritical case, 0 < gamma < 1, we obtain new local wellposedness results and smoothing properties of solutions. In the critical case, gamma = 1, we prove the global wellposedness for initial data having a small L-x(1) norm. In the subcritical case, gamma > 1, we prove global wellposedness and smoothing of solutions with general L-x(1) initial data.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Revista Matematica Iberoamericana
Publisher:	European Mathematical Society Publishing House
ISSN:	0213-2230
Official Date:	2010
Dates:	Date Event 2010 Published
Volume:	Vol.26
Number:	No.1
Number of Pages:	34
Page Range:	pp. 261-294
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Mathematics Department of the University of Iowa, National Science Foundation, Ministerio de Educacion y Ciencia (Spain)
Grant number:	DMS-0635607, DMS-0908032, MTM2005-05980

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