Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-06-28T13:22:19Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150439 |
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