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

Abstract 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 ω θ = ∂ z u r − ∂ r u z , ∂ r u r , ∂ z u z or ∂ r u θ .

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