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Wellposedness and regularity of solutions of an aggregation equation
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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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Official URL: http://projecteuclid.org/euclid.rmi/1266330124
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 > Mathematics |
| Journal or Publication Title: | Revista Matematica Iberoamericana |
| Publisher: | European Mathematical Society Publishing House |
| ISSN: | 0213-2230 |
| Date: | 2010 |
| 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 |
| URI: | http://wrap.warwick.ac.uk/id/eprint/5802 |
Data sourced from Thomson Reuters' Web of Knowledge
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