Global well-posedness of slightly supercritical active scalar equations


Journal Article

The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasigeostrophic (SQG) and Burgers equations, when the diffusion term is supercritical by a symbol with roughly logarithmic behavior at infinity. We show that the result is sharp for the Burgers equation. We also prove global regularity for a slightly supercritical two-dimensional Euler equation. Our main tool is a nonlocal maximum principle which controls a certain modulus of continuity of the solutions. ©2014 Mathematical Sciences Publishers.

Full Text

Duke Authors

Cited Authors

  • Dabkowski, M; Kiselev, A; Silvestre, L; Vicol, V

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 7 / 1

Start / End Page

  • 43 - 72

Electronic International Standard Serial Number (EISSN)

  • 1948-206X

International Standard Serial Number (ISSN)

  • 2157-5045

Digital Object Identifier (DOI)

  • 10.2140/apde.2014.7.43

Citation Source

  • Scopus