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

Author(s): Yong Zhou
Journal: Proc. Amer. Math. Soc. 134 (2006), 149-156.
MSC (2000): Primary 35B45, 35B65, 76D05
Posted: August 19, 2005
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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: 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
Posted: August 19, 2005
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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