English

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 LpL^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.

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}
}