REGULARITY OF 3D AXISYMMETRIC NAVIER-STOKES EQUATIONS

In this paper, we study the three-dimensional axisymmetric NavierStokes system with nonzero swirl. By establishing a new key inequality for the pair (omega(r)/r, omega(theta)/r), we get several Prodi-Serrin type regularity criteria based on the angular velocity, u(theta). Moreover, we obtain the global well-posedness result if the initial angular velocity u(0)(theta) is appropriate small in the critical space L-3 (R-3). Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say omega(3) or u(3).