Blow up and regularity for fractal burgers equation

Journal Article (Journal Article)

The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian α < 1/2, and global existence as well as analyticity of solution for α ≥ 1/2. We also prove the existence of solutions with very rough initial data uo ∈ Lp, 1 < p < ∞. Many of the results can be extended to a more general class of equations, including the surface quasi-geostrophic equation. ©2008 International Press.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Nazarov, F; Shterenberg, R

Published Date

  • January 1, 2008

Published In

Volume / Issue

  • 5 / 3

Start / End Page

  • 211 - 240

International Standard Serial Number (ISSN)

  • 1548-159X

Digital Object Identifier (DOI)

  • 10.4310/DPDE.2008.v5.n3.a2

Citation Source

  • Scopus