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

Hou, Thomas Y. and Lei, Zhen and Li, Congming (2008) Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data. Communications in Partial Differential Equation, 33 (9). pp. 1622-1637. ISSN 0360-5302. doi:10.1080/03605300802108057.

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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 Lp 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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Additional Information:© 2008 Taylor & Francis. We would like to thank Profs. Charles Fefferman and Fanghua Lin for their interests in this work and for some stimulating discussions. The research was in part supported by NSF under the NSF FRG grant DMS-0353838 and ITR Grant ACI-0204932.
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Subject Keywords:Large anisotropic data; Navier-Stokes equations
Issue or Number:9
Classification Code:Mathematics Subject Classification: 76D03; 76D05; 35Q30
Record Number:CaltechAUTHORS:20091014-100827184
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16343
Deposited By: Joy Painter
Deposited On:19 Oct 2009 00:29
Last Modified:08 Nov 2021 23:26

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