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On a one-dimensional nonlocal flux with fractional dissipation
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Li, Dong and Rodrigo, Jose L.. (2011) On a one-dimensional nonlocal flux with fractional dissipation. SIAM Journal on Mathematical Analysis, Vol.43 (No.1). pp. 507-526. ISSN 0036-1410
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Official URL: http://dx.doi.org/10.1137/100794924
Abstract
We study a class of one-dimensional conservation laws with nonlocal flux and fractional dissipation: partial derivative(t)theta - (theta H theta)(x) = -nu(-partial derivative(xx))(gamma/2)theta, where H is the Hilbert transform. In the regime nu > 0 and 1 < gamma <= 2, we prove local existence and regularity of solutions regardless of the sign of the initial data. For all values nu >= 0 and 0 <= gamma <= 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 Cordoba [Adv. Math., 219 (2008), pp. 1916-1936].
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | SIAM Journal on Mathematical Analysis |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 0036-1410 |
| Date: | 2011 |
| Volume: | Vol.43 |
| Number: | No.1 |
| Page Range: | pp. 507-526 |
| Identification Number: | 10.1137/100794924 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | NSF , University of Iowa , Mathematics Department of University of Iowa , Spanish Ministry of Education |
| Grant number: | NSF (0908032), Spanish Ministry of Education (MTM2005-05980-C02-01) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/41510 |
Data sourced from Thomson Reuters' Web of Knowledge
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