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arXiv · 0901.3486

Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data

Thomas Y. Hou·Zhen Lei·Congming Li
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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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Thomas Y. Hou, Zhen Lei, Congming Li. 2009-01-24. Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data. https://arxiv.org/abs/0901.3486

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