Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data
Analysis of PDEs
2009-01-24 v2
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 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.
Keywords
Cite
@article{arxiv.0901.3486,
title = {Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data},
author = {Thomas Y. Hou and Zhen Lei and Congming Li},
journal= {arXiv preprint arXiv:0901.3486},
year = {2009}
}