  We point out some criteria that imply regularity of axisymmetric solutions to
Navier-Stokes equations. We show that boundedness of
$\|{v_{r}}/{\sqrt{r^3}}\|_{L_2({\rm R}^3\times (0,T))}$ as well as boundedness
of $\|{\omega_{\varphi}}/{\sqrt{r}}\|_{L_2({\rm R}^3\times (0,T))},$ where
$v_r$ is the radial component of velocity and $\omega_{\varphi}$ is the angular
component of vorticity, imply regularity of weak solutions.
