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

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

2009-01-22

arxiv.org/abs/0901.3486v2

Communications in Partial Differential Equations, 33 (2008), no. 9, 1622-1637

Mathematics

Analysis of PDEs

Scientific paper

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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