Proves global regularity for axisymmetric 3D Navier-Stokes flows with swirl by controlling near-axis source terms via circulation identities and Hardy estimates.
Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data
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abstract
In this paper, we study the 3D axi-symmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some $L^p$ norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction between the angular velocity and the angular vorticity fields.
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2026 1verdicts
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Global Regularity for Axisymmetric Navier--Stokes Flows with Swirl
Proves global regularity for axisymmetric 3D Navier-Stokes flows with swirl by controlling near-axis source terms via circulation identities and Hardy estimates.