Regularity for the axisymmetric Navier-Stokes equations
In this article, we establish a regularity criterion for the Navier-Stokes system with axisymmetric initial data. It is proved that if the local axisymmetric smooth solution $u$ satisfies ${\|u^\theta\|_{L^{\alpha}(0,T; L^{\beta})}}<\infty$ , where $\frac{2}{\alpha}+\frac{3}{\beta} \leq 1 $,...
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| Format: | Article |
| Language: | English |
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Texas State University
2015-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/250/abstr.html |
| _version_ | 1818945302923575296 |
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| author | Peng Wang |
| author_facet | Peng Wang |
| author_sort | Peng Wang |
| collection | DOAJ |
| description | In this article, we establish a regularity criterion for the Navier-Stokes
system with axisymmetric initial data. It is proved that if the
local axisymmetric smooth solution $u$ satisfies
${\|u^\theta\|_{L^{\alpha}(0,T; L^{\beta})}}<\infty$ , where
$\frac{2}{\alpha}+\frac{3}{\beta} \leq 1 $, and
$3 < \beta \leq \infty$, then the strong solution keeps smoothness up
to time T. |
| first_indexed | 2024-12-20T07:56:58Z |
| format | Article |
| id | doaj.art-29dd5f7bc7f04ddda0c4b24d52527f4c |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T07:56:58Z |
| publishDate | 2015-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-29dd5f7bc7f04ddda0c4b24d52527f4c2022-12-21T19:47:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-09-012015250,19Regularity for the axisymmetric Navier-Stokes equationsPeng Wang0 Zhejiang Normal Univ.,Zhejiang, China In this article, we establish a regularity criterion for the Navier-Stokes system with axisymmetric initial data. It is proved that if the local axisymmetric smooth solution $u$ satisfies ${\|u^\theta\|_{L^{\alpha}(0,T; L^{\beta})}}<\infty$ , where $\frac{2}{\alpha}+\frac{3}{\beta} \leq 1 $, and $3 < \beta \leq \infty$, then the strong solution keeps smoothness up to time T.http://ejde.math.txstate.edu/Volumes/2015/250/abstr.htmlNavier-Stokes equationsaxi-symmetric flowregularity criterion |
| spellingShingle | Peng Wang Regularity for the axisymmetric Navier-Stokes equations Electronic Journal of Differential Equations Navier-Stokes equations axi-symmetric flow regularity criterion |
| title | Regularity for the axisymmetric Navier-Stokes equations |
| title_full | Regularity for the axisymmetric Navier-Stokes equations |
| title_fullStr | Regularity for the axisymmetric Navier-Stokes equations |
| title_full_unstemmed | Regularity for the axisymmetric Navier-Stokes equations |
| title_short | Regularity for the axisymmetric Navier-Stokes equations |
| title_sort | regularity for the axisymmetric navier stokes equations |
| topic | Navier-Stokes equations axi-symmetric flow regularity criterion |
| url | http://ejde.math.txstate.edu/Volumes/2015/250/abstr.html |
| work_keys_str_mv | AT pengwang regularityfortheaxisymmetricnavierstokesequations |