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- Publisher Website: 10.1512/iumj.2009.58.3505
- Scopus: eid_2-s2.0-67249097393
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Article: Finite time singularities and global well-posedness for fractal Burgers equations
Title | Finite time singularities and global well-posedness for fractal Burgers equations |
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Authors | |
Keywords | Burgers equation Finite-time singularaties Global well-posedness spatial analyticity |
Issue Date | 2009 |
Citation | Indiana University Mathematics Journal, 2009, v. 58, n. 2, p. 807-821 How to Cite? |
Abstract | Burgers equations with fractional dissipation on ℝ x ℝ+ or on ℝ1 x ℝR+ are studied. In the supercritical dissipative case, we show that with very generic initial data, the equation is locally well-posed and its solution develops gradient blow-up in finite time. In the critical dissipative case, the equation is globally well-posed with arbitrary initial data in H1/2. Finally, in the subcritical dissipative case, we prove that with initial data in the scaling-invariant Lebesgue space, the equation is globally well-posed. Moreover, the solution is spatial analytic and has optimal Gevrey regularity in the time variable. |
Persistent Identifier | http://hdl.handle.net/10722/326778 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.272 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Dong, Hongjie | - |
dc.contributor.author | Du, Dapeng | - |
dc.contributor.author | Li, Dong | - |
dc.date.accessioned | 2023-03-31T05:26:27Z | - |
dc.date.available | 2023-03-31T05:26:27Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Indiana University Mathematics Journal, 2009, v. 58, n. 2, p. 807-821 | - |
dc.identifier.issn | 0022-2518 | - |
dc.identifier.uri | http://hdl.handle.net/10722/326778 | - |
dc.description.abstract | Burgers equations with fractional dissipation on ℝ x ℝ+ or on ℝ1 x ℝR+ are studied. In the supercritical dissipative case, we show that with very generic initial data, the equation is locally well-posed and its solution develops gradient blow-up in finite time. In the critical dissipative case, the equation is globally well-posed with arbitrary initial data in H1/2. Finally, in the subcritical dissipative case, we prove that with initial data in the scaling-invariant Lebesgue space, the equation is globally well-posed. Moreover, the solution is spatial analytic and has optimal Gevrey regularity in the time variable. | - |
dc.language | eng | - |
dc.relation.ispartof | Indiana University Mathematics Journal | - |
dc.subject | Burgers equation | - |
dc.subject | Finite-time singularaties | - |
dc.subject | Global well-posedness | - |
dc.subject | spatial analyticity | - |
dc.title | Finite time singularities and global well-posedness for fractal Burgers equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1512/iumj.2009.58.3505 | - |
dc.identifier.scopus | eid_2-s2.0-67249097393 | - |
dc.identifier.volume | 58 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 807 | - |
dc.identifier.epage | 821 | - |
dc.identifier.isi | WOS:000265899500012 | - |