Lecture Notes in Mathematics
Small Scale Creation in Active Scalars
Publication
, Chapter
Kiselev, AA
January 1, 2020
The focus of the course is on small scale formation in solutions of the incompressible Euler equation of fluid dynamics and associated models. We first review the regularity results and examples of small scale growth in two dimensions. Then we discuss a specific singular scenario for the three-dimensional Euler equation discovered by Hou and Luo, and analyze some associated models. Finally, we will also talk about the surface quasi-geostrophic (SQG) equation, and construct an example of singularity formation in the modified SQG patch solutions as well as examples of unbounded growth of derivatives for the smooth solutions.
Duke Scholars
DOI
Publication Date
January 1, 2020
Volume
2272
Start / End Page
125 / 161
Related Subject Headings
- General Mathematics
- 01 Mathematical Sciences
Citation
APA
Chicago
ICMJE
MLA
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Kiselev, A. A. (2020). Small Scale Creation in Active Scalars. In Lecture Notes in Mathematics (Vol. 2272, pp. 125–161). https://doi.org/10.1007/978-3-030-54899-5_4
Kiselev, A. A. “Small Scale Creation in Active Scalars.” In Lecture Notes in Mathematics, 2272:125–61, 2020. https://doi.org/10.1007/978-3-030-54899-5_4.
Kiselev AA. Small Scale Creation in Active Scalars. In: Lecture Notes in Mathematics. 2020. p. 125–61.
Kiselev, A. A. “Small Scale Creation in Active Scalars.” Lecture Notes in Mathematics, vol. 2272, 2020, pp. 125–61. Scopus, doi:10.1007/978-3-030-54899-5_4.
Kiselev AA. Small Scale Creation in Active Scalars. Lecture Notes in Mathematics. 2020. p. 125–161.
DOI
Publication Date
January 1, 2020
Volume
2272
Start / End Page
125 / 161
Related Subject Headings
- General Mathematics
- 01 Mathematical Sciences