Global well-posedness of slightly supercritical active scalar equations
Publication
, Journal Article
Dabkowski, M; Kiselev, A; Silvestre, L; Vicol, V
Published in: Analysis and Pde
January 1, 2014
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.
Duke Scholars
Published In
Analysis and Pde
DOI
EISSN
1948-206X
ISSN
2157-5045
Publication Date
January 1, 2014
Volume
7
Issue
1
Start / End Page
43 / 72
Related Subject Headings
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Dabkowski, M., Kiselev, A., Silvestre, L., & Vicol, V. (2014). Global well-posedness of slightly supercritical active scalar equations. Analysis and Pde, 7(1), 43–72. https://doi.org/10.2140/apde.2014.7.43
Dabkowski, M., A. Kiselev, L. Silvestre, and V. Vicol. “Global well-posedness of slightly supercritical active scalar equations.” Analysis and Pde 7, no. 1 (January 1, 2014): 43–72. https://doi.org/10.2140/apde.2014.7.43.
Dabkowski M, Kiselev A, Silvestre L, Vicol V. Global well-posedness of slightly supercritical active scalar equations. Analysis and Pde. 2014 Jan 1;7(1):43–72.
Dabkowski, M., et al. “Global well-posedness of slightly supercritical active scalar equations.” Analysis and Pde, vol. 7, no. 1, Jan. 2014, pp. 43–72. Scopus, doi:10.2140/apde.2014.7.43.
Dabkowski M, Kiselev A, Silvestre L, Vicol V. Global well-posedness of slightly supercritical active scalar equations. Analysis and Pde. 2014 Jan 1;7(1):43–72.
Published In
Analysis and Pde
DOI
EISSN
1948-206X
ISSN
2157-5045
Publication Date
January 1, 2014
Volume
7
Issue
1
Start / End Page
43 / 72
Related Subject Headings
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics