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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |