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Article: Wellposedness and regularity of solutions of an aggregation equation
Title | Wellposedness and regularity of solutions of an aggregation equation |
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Authors | |
Keywords | Aggregation equations Higher regularity Well-posedness |
Issue Date | 2010 |
Citation | Revista Matematica Iberoamericana, 2010, v. 26, n. 1, p. 261-294 How to Cite? |
Abstract | We consider an aggregation equation in ℝd, d ≥ 2 with fractional dissipation: ut + ∇· (u∇K*u) = -vΛΥu, where v≥ 0, 0<Υ≤2 and K(x) = e-|x| In the supercritical case, 0 < Υ < 1, we obtain new local wellposedness results and smoothing properties of solutions. In the critical case, Υ = 1, we prove the global wellposedness for initial data having a small L1x norm. In the subcritical case, Υ > 1, we prove global wellposedness and smoothing of solutions with general L 1x initial data. |
Persistent Identifier | http://hdl.handle.net/10722/326807 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 1.458 |
DC Field | Value | Language |
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dc.contributor.author | Li, Dong | - |
dc.contributor.author | Rodrigo, José L. | - |
dc.date.accessioned | 2023-03-31T05:26:40Z | - |
dc.date.available | 2023-03-31T05:26:40Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Revista Matematica Iberoamericana, 2010, v. 26, n. 1, p. 261-294 | - |
dc.identifier.issn | 0213-2230 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326807 | - |
dc.description.abstract | We consider an aggregation equation in ℝd, d ≥ 2 with fractional dissipation: ut + ∇· (u∇K*u) = -vΛΥu, where v≥ 0, 0<Υ≤2 and K(x) = e-|x| In the supercritical case, 0 < Υ < 1, we obtain new local wellposedness results and smoothing properties of solutions. In the critical case, Υ = 1, we prove the global wellposedness for initial data having a small L1x norm. In the subcritical case, Υ > 1, we prove global wellposedness and smoothing of solutions with general L 1x initial data. | - |
dc.language | eng | - |
dc.relation.ispartof | Revista Matematica Iberoamericana | - |
dc.subject | Aggregation equations | - |
dc.subject | Higher regularity | - |
dc.subject | Well-posedness | - |
dc.title | Wellposedness and regularity of solutions of an aggregation equation | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.4171/RMI/601 | - |
dc.identifier.scopus | eid_2-s2.0-77951117235 | - |
dc.identifier.volume | 26 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 261 | - |
dc.identifier.epage | 294 | - |