Regularity and blow up for active scalars


Journal Article (Review)

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.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A

Published Date

  • January 1, 2010

Published In

Volume / Issue

  • 5 / 4

Start / End Page

  • 225 - 255

Electronic International Standard Serial Number (EISSN)

  • 1760-6101

International Standard Serial Number (ISSN)

  • 0973-5348

Digital Object Identifier (DOI)

  • 10.1051/mmnp/20105410

Citation Source

  • Scopus