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
APA
Chicago
ICMJE
MLA
NLM
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