A new regularity criterion for the Navier-Stokes equations in terms of the two components of the velocity
This paper establishes a new regularity criterion for the Navier-Stokes equation in terms of two velocity components. We show that if the two velocity components $\widetilde{u}=\left( u_{1},u_{2},0\right) $ satisfy \begin{equation*} \int_{0}^{T}\Vert \tilde{u}(s)\Vert _{\dot{B}_{\infty ,\infty }...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2016-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4452 |
| Summary: | This paper establishes a new regularity criterion for the Navier-Stokes equation in terms of two velocity components. We show that if the two velocity components $\widetilde{u}=\left( u_{1},u_{2},0\right) $ satisfy
\begin{equation*}
\int_{0}^{T}\Vert \tilde{u}(s)\Vert _{\dot{B}_{\infty ,\infty
}^{0}}^{2}ds<\infty ,
\end{equation*}
then the solution can be smoothly extended after $t=T$. This gives an aswer to an open problem in [B. Q. Dong, Z. Zhang, Nonlinear Anal. Real World Appl. 11(2010), 2415-2421]. |
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| ISSN: | 1417-3875 1417-3875 |