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- Publisher Website: 10.3934/cpaa.2010.9.1591
- Scopus: eid_2-s2.0-82155184395
- WOS: WOS:000281805200007
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Article: Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels
Title | Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels |
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Authors | |
Keywords | Aggregation Blowup Singular kernel |
Issue Date | 2010 |
Citation | Communications on Pure and Applied Analysis, 2010, v. 9, n. 6, p. 1591-1606 How to Cite? |
Abstract | We consider a nonlocal evolution equation in R2: ℓtu +δ • (uK * u) = 0, where K(x) = μ x |x| , μ = ±1 and 1 > α > 2. We study wellposedness, continuation/blowup criteria and smoothness of solutions in Sobolev spaces. In the repulsive case (μ = 1), by using the sharp blowup criteria, we prove global wellposedness for any positive large initial data. In the attractive case (μ = -1), by using a novel free energy inequality together with a mass localization technique, we construct finite time blowups for a large class of smooth initial data. |
Persistent Identifier | http://hdl.handle.net/10722/326878 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.744 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, Dong | - |
dc.contributor.author | Zhang, Xiaoyi | - |
dc.date.accessioned | 2023-03-31T05:27:11Z | - |
dc.date.available | 2023-03-31T05:27:11Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Communications on Pure and Applied Analysis, 2010, v. 9, n. 6, p. 1591-1606 | - |
dc.identifier.issn | 1534-0392 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326878 | - |
dc.description.abstract | We consider a nonlocal evolution equation in R2: ℓtu +δ • (uK * u) = 0, where K(x) = μ x |x| , μ = ±1 and 1 > α > 2. We study wellposedness, continuation/blowup criteria and smoothness of solutions in Sobolev spaces. In the repulsive case (μ = 1), by using the sharp blowup criteria, we prove global wellposedness for any positive large initial data. In the attractive case (μ = -1), by using a novel free energy inequality together with a mass localization technique, we construct finite time blowups for a large class of smooth initial data. | - |
dc.language | eng | - |
dc.relation.ispartof | Communications on Pure and Applied Analysis | - |
dc.subject | Aggregation | - |
dc.subject | Blowup | - |
dc.subject | Singular kernel | - |
dc.title | Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.3934/cpaa.2010.9.1591 | - |
dc.identifier.scopus | eid_2-s2.0-82155184395 | - |
dc.identifier.volume | 9 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 1591 | - |
dc.identifier.epage | 1606 | - |
dc.identifier.eissn | 1553-5258 | - |
dc.identifier.isi | WOS:000281805200007 | - |