Regularity and blow up for active scalars
Publication
, Journal Article
Kiselev, A
Published in: Mathematical Modelling of Natural Phenomena
January 1, 2010
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow up in the supercritical regime. © EDP Sciences, 2010.
Duke Scholars
Published In
Mathematical Modelling of Natural Phenomena
DOI
EISSN
1760-6101
ISSN
0973-5348
Publication Date
January 1, 2010
Volume
5
Issue
4
Start / End Page
225 / 255
Related Subject Headings
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Kiselev, A. (2010). Regularity and blow up for active scalars. Mathematical Modelling of Natural Phenomena, 5(4), 225–255. https://doi.org/10.1051/mmnp/20105410
Kiselev, A. “Regularity and blow up for active scalars.” Mathematical Modelling of Natural Phenomena 5, no. 4 (January 1, 2010): 225–55. https://doi.org/10.1051/mmnp/20105410.
Kiselev A. Regularity and blow up for active scalars. Mathematical Modelling of Natural Phenomena. 2010 Jan 1;5(4):225–55.
Kiselev, A. “Regularity and blow up for active scalars.” Mathematical Modelling of Natural Phenomena, vol. 5, no. 4, Jan. 2010, pp. 225–55. Scopus, doi:10.1051/mmnp/20105410.
Kiselev A. Regularity and blow up for active scalars. Mathematical Modelling of Natural Phenomena. 2010 Jan 1;5(4):225–255.
Published In
Mathematical Modelling of Natural Phenomena
DOI
EISSN
1760-6101
ISSN
0973-5348
Publication Date
January 1, 2010
Volume
5
Issue
4
Start / End Page
225 / 255
Related Subject Headings
- 4901 Applied mathematics
- 0102 Applied Mathematics