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

 

On regularity criteria in terms of pressure for the Navier-Stokes equations in $\mathbb{R} ^3$


Author: Yong Zhou
Journal: Proc. Amer. Math. Soc. 134 (2006), 149-156
MSC (2000): Primary 35B45, 35B65, 76D05
Published electronically: August 19, 2005
MathSciNet review: 2170554
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Abstract: In this paper we establish a Serrin-type regularity criterion on the gradient of pressure for the weak solutions to the Navier-Stokes equations in $\mathbb{R} ^3$. It is proved that if the gradient of pressure belongs to $L^{\alpha,\gamma}$ with $2/\alpha+3/\gamma \leq 3$, $1\leq \gamma \leq \infty$, then the weak solution is actually regular. Moreover, we give a much simpler proof of the regularity criterion on the pressure, which was showed recently by Berselli and Galdi (Proc. Amer. Math. Soc. 130 (2002), no. 12, 3585-3595).


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Additional Information

Yong Zhou
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
Email: yzhou@math.ecnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08312-7
PII: S 0002-9939(05)08312-7
Keywords: Navier-Stokes equations, regularity criterion, integrability of pressure, a priori estimates
Received by editor(s): February 3, 2004
Published electronically: August 19, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.