Several new regularity criteria for the axisymmetric Navier-Stokes equations with swirl

In this paper, we consider the axisymmetric Navier-Stokes equations with swirl, and show that the global regularity is ensured if we add some (weighted) integrable conditions on ωθ=∂zur−∂ruz, ∂rur, ∂zuz or ∂ruθ.