arXiv:0901.3486 [math.AP]AbstractReferencesReviewsResources
Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data
Thomas Y. Hou, Zhen Lei, Congming Li
Published 2009-01-22, updated 2009-01-24Version 2
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.
Journal: Communications in Partial Differential Equations, 33 (2008), no. 9, 1622-1637
Categories: math.AP
Keywords: 3d axi-symmetric navier-stokes equations, global regularity, anisotropic data, large anisotropic initial data, 3d navier-stokes equations
Tags: journal article
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