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Article: On a one-dimensional nonlocal flux with fractional dissipation
| Title | On a one-dimensional nonlocal flux with fractional dissipation |
|---|---|
| Authors | |
| Keywords | Blow-up Fractional dissipation Hilbert transform Quasi-geostrophic equations |
| Issue Date | 2011 |
| Citation | SIAM Journal on Mathematical Analysis, 2011, v. 43, n. 1, p. 507-526 How to Cite? |
| Abstract | We study a class of one-dimensional conservation laws with nonlocal flux and fractional dissipation: ∂tθ - (θHθ) x = -ν(-∂xx)γ/2θ, where H is the Hilbert transform. In the regime ν > 0 and 1 < γ ≤ 2, we prove local existence and regularity of solutions regardless of the sign of the initial data. For all values ν ≥ 0 and 0 ≤ γ ≤ 2, we construct a certain class of positive smooth initial data with sufficiently localized mass, such that corresponding solutions blow up in finite time. This extends recent results of Castro and Córdoba [Adv. Math., 219 (2008), pp. 1916-1936]. Copyright © 2011 by SIAM. |
| Persistent Identifier | http://hdl.handle.net/10722/327474 |
| ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 2.374 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Li, Dong | - |
| dc.contributor.author | Rodrigo, José L. | - |
| dc.date.accessioned | 2023-03-31T05:31:36Z | - |
| dc.date.available | 2023-03-31T05:31:36Z | - |
| dc.date.issued | 2011 | - |
| dc.identifier.citation | SIAM Journal on Mathematical Analysis, 2011, v. 43, n. 1, p. 507-526 | - |
| dc.identifier.issn | 0036-1410 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/327474 | - |
| dc.description.abstract | We study a class of one-dimensional conservation laws with nonlocal flux and fractional dissipation: ∂tθ - (θHθ) x = -ν(-∂xx)γ/2θ, where H is the Hilbert transform. In the regime ν > 0 and 1 < γ ≤ 2, we prove local existence and regularity of solutions regardless of the sign of the initial data. For all values ν ≥ 0 and 0 ≤ γ ≤ 2, we construct a certain class of positive smooth initial data with sufficiently localized mass, such that corresponding solutions blow up in finite time. This extends recent results of Castro and Córdoba [Adv. Math., 219 (2008), pp. 1916-1936]. Copyright © 2011 by SIAM. | - |
| dc.language | eng | - |
| dc.relation.ispartof | SIAM Journal on Mathematical Analysis | - |
| dc.subject | Blow-up | - |
| dc.subject | Fractional dissipation | - |
| dc.subject | Hilbert transform | - |
| dc.subject | Quasi-geostrophic equations | - |
| dc.title | On a one-dimensional nonlocal flux with fractional dissipation | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1137/100794924 | - |
| dc.identifier.scopus | eid_2-s2.0-79952297110 | - |
| dc.identifier.volume | 43 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | 507 | - |
| dc.identifier.epage | 526 | - |
| dc.identifier.isi | WOS:000287696400019 | - |