On some regularity criteria for axisymmetric Navier-Stokes equations

Abstract

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

18 pages