Nonlocal maximum principles for active scalars


Journal Article

Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations are 2D Euler, Burgers, and 2D surface quasi-geostrophic equations. Many questions about regularity and properties of solutions of these equations remain open. We develop the idea of nonlocal maximum principle introduced in Kiselev, Nazarov and Volberg (2007) [19], formulating a more general criterion and providing new applications. The most interesting application is finite time regularization of weak solutions in the supercritical regime. © 2011 Elsevier Inc.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A

Published Date

  • August 1, 2011

Published In

Volume / Issue

  • 227 / 5

Start / End Page

  • 1806 - 1826

Electronic International Standard Serial Number (EISSN)

  • 1090-2082

International Standard Serial Number (ISSN)

  • 0001-8708

Digital Object Identifier (DOI)

  • 10.1016/j.aim.2011.03.019

Citation Source

  • Scopus