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Blow up and regularity for fractal burgers equation

Publication ,  Journal Article
Kiselev, A; Nazarov, F; Shterenberg, R
Published in: Dynamics of Partial Differential Equations
January 1, 2008

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.

Duke Scholars

Published In

Dynamics of Partial Differential Equations

DOI

ISSN

1548-159X

Publication Date

January 1, 2008

Volume

5

Issue

3

Start / End Page

211 / 240

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics
 

Citation

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Kiselev, A., Nazarov, F., & Shterenberg, R. (2008). Blow up and regularity for fractal burgers equation. Dynamics of Partial Differential Equations, 5(3), 211–240. https://doi.org/10.4310/DPDE.2008.v5.n3.a2
Kiselev, A., F. Nazarov, and R. Shterenberg. “Blow up and regularity for fractal burgers equation.” Dynamics of Partial Differential Equations 5, no. 3 (January 1, 2008): 211–40. https://doi.org/10.4310/DPDE.2008.v5.n3.a2.
Kiselev A, Nazarov F, Shterenberg R. Blow up and regularity for fractal burgers equation. Dynamics of Partial Differential Equations. 2008 Jan 1;5(3):211–40.
Kiselev, A., et al. “Blow up and regularity for fractal burgers equation.” Dynamics of Partial Differential Equations, vol. 5, no. 3, Jan. 2008, pp. 211–40. Scopus, doi:10.4310/DPDE.2008.v5.n3.a2.
Kiselev A, Nazarov F, Shterenberg R. Blow up and regularity for fractal burgers equation. Dynamics of Partial Differential Equations. 2008 Jan 1;5(3):211–240.

Published In

Dynamics of Partial Differential Equations

DOI

ISSN

1548-159X

Publication Date

January 1, 2008

Volume

5

Issue

3

Start / End Page

211 / 240

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics