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Article: Refined blowup criteria and nonsymmetric blowup of an aggregation equation
Title | Refined blowup criteria and nonsymmetric blowup of an aggregation equation |
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Authors | |
Keywords | Aggregation equations Blowup Blowup criteria Fractional dissipation |
Issue Date | 2009 |
Citation | Advances in Mathematics, 2009, v. 220, n. 6, p. 1717-1738 How to Cite? |
Abstract | We consider an aggregation equation in Rd, d ≥ 2, with fractional dissipation: ut + ∇ ṡ (u ∇ K * u) = - ν Λγ u, where ν ≥ 0, 0 < γ < 1, and K (x) = e- | x |. We prove a refined blowup criteria by which the global existence of solutions is controlled by its Lxq norm, for any frac(d, d - 1) ≤ q ≤ ∞. 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 ν = 0 and the supercritical case ν > 0 and 0 < γ < 1. Additionally, we present new proofs of blowup which does not use free energy arguments. © 2008 Elsevier Inc. All rights reserved. |
Persistent Identifier | http://hdl.handle.net/10722/326766 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.022 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, Dong | - |
dc.contributor.author | Rodrigo, Jose L. | - |
dc.date.accessioned | 2023-03-31T05:26:22Z | - |
dc.date.available | 2023-03-31T05:26:22Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Advances in Mathematics, 2009, v. 220, n. 6, p. 1717-1738 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326766 | - |
dc.description.abstract | We consider an aggregation equation in Rd, d ≥ 2, with fractional dissipation: ut + ∇ ṡ (u ∇ K * u) = - ν Λγ u, where ν ≥ 0, 0 < γ < 1, and K (x) = e- | x |. We prove a refined blowup criteria by which the global existence of solutions is controlled by its Lxq norm, for any frac(d, d - 1) ≤ q ≤ ∞. 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 ν = 0 and the supercritical case ν > 0 and 0 < γ < 1. Additionally, we present new proofs of blowup which does not use free energy arguments. © 2008 Elsevier Inc. All rights reserved. | - |
dc.language | eng | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.subject | Aggregation equations | - |
dc.subject | Blowup | - |
dc.subject | Blowup criteria | - |
dc.subject | Fractional dissipation | - |
dc.title | Refined blowup criteria and nonsymmetric blowup of an aggregation equation | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.aim.2008.10.016 | - |
dc.identifier.scopus | eid_2-s2.0-60349124484 | - |
dc.identifier.volume | 220 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 1717 | - |
dc.identifier.epage | 1738 | - |
dc.identifier.eissn | 1090-2082 | - |
dc.identifier.isi | WOS:000264104800003 | - |