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Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. (English) Zbl 1146.76010

Summary: We study 3D axisymmetric 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 on 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 angular vorticity fields.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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