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Weighted regularity criteria for the three-dimensional Navier—Stokes equations

Published online by Cambridge University Press:  26 May 2009

Yong Zhou
Yong Zhou
Affiliation:
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China (yzhoumath@zjnu.cn)
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Abstract

We establish some regularity criteria in terms of the velocity field with weight for the Navier—Stokes equations in ℝ3. It is proved that if the weak solution satisfies

or

then the weak solution actually is regular up to time T.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 3 , June 2009 , pp. 661 - 671
Copyright
Copyright © Royal Society of Edinburgh 2009

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