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Communications in Partial Differential Equations

Volume 33, Issue 9, 2008

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

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DOI:
10.1080/03605300802108057
Thomas Y. Houa*, Zhen Leia & Congming Lib

pages 1622-1637

Available online: 20 Aug 2008
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Abstract

In this paper, we study the 3D axisymmetric 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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  • Citation information:
  • Available online: 20 Aug 2008

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Author affiliations

  • a Applied and Computational Mathematics, Caltech, Pasadena, California, USA
  • b Department of Applied Mathematics, University of Colorado, Boulder, Colorado, USA

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