Electron. J. Diff. Equ., Vol. 2015 (2015), No. 250, pp. 1-9.

Regularity for the axisymmetric Navier-Stokes equations

Peng Wang

Abstract:
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.

Submitted June 11, 2015. Published September 25, 2015.
Math Subject Classifications: 35Q30, 76D03.
Key Words: Navier-Stokes equations; axi-symmetric flow; regularity criterion.

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Peng Wang
Department of Mathematics
Zhejiang Normal University
Jinhua 321004, Zhejiang, China
email: wpmath2013@gmail.com

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