| Title:
|
Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations (English) |
| Author:
|
Zhang, Zujin |
| Author:
|
Tong, Chenxuan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
485-507 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $$ |\omega ^r(x,t)|+|\omega ^z(r,t)|\leq \frac {C}{r^{10}},\quad 0<r\leq \frac {1}{2}. $$ By employing the dimension reduction technique by Lei-Navas-Zhang, and analyzing $\omega ^r$, $\omega ^z$ and $\omega ^\theta /r$ on different hollow cylinders, we are able to improve it and obtain $$ |\omega ^r(x,t)|+|\omega ^z(r,t)|\leq \frac {C|{\rm ln} r|}{r^{17/2}},\quad 0<r\leq \frac 12. $$ (English) |
| Keyword:
|
axisymmetric Navier-Stokes equations |
| Keyword:
|
weighted a priori bounds |
| MSC:
|
35B65 |
| MSC:
|
35Q35 |
| MSC:
|
76D03 |
| idZBL:
|
Zbl 07584082 |
| idMR:
|
MR4444789 |
| DOI:
|
10.21136/AM.2021.0344-20 |
| . |
| Date available:
|
2022-06-28T13:22:19Z |
| Last updated:
|
2024-09-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150439 |
| . |
| Reference:
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