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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity criterion via the pressure on weak solutions to the 3D Navier-Stokes equations


Authors: Chen Qionglei and Zhang Zhifei
Journal: Proc. Amer. Math. Soc. 135 (2007), 1829-1837
MSC (2000): Primary 35Q30, 35B65, 76D03
Published electronically: December 29, 2006
MathSciNet review: 2286093
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Abstract: We consider the regularity of weak solutions to the Navier-Stokes equations in $ \mathbb{R}^3$. Let $ u$ be a Leray-Hopf weak solution. It is proved that $ u$ becomes a regular solution if the pressure $ p \in L^1(0,T; \dot B^0_{\infty,\infty})$.


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Additional Information

Chen Qionglei
Affiliation: Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China
Email: chen_qionglei@iapcm.ac.cn

Zhang Zhifei
Affiliation: School of Mathematical Science, Peking University, Beijing 100871, People’s Republic of China
Email: zfzhang@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08663-1
PII: S 0002-9939(06)08663-1
Received by editor(s): May 15, 2004
Received by editor(s) in revised form: February 7, 2006
Published electronically: December 29, 2006
Additional Notes: The second author is supported by National Natural Science Foundation of China (10601002)
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society