Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 250, pp. 1-9.
Title: Regularity for the axisymmetric Navier-Stokes equations
Author: Peng Wang (Zhejiang Normal Univ.,Zhejiang, China)
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.