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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
Posted: August 19, 2005
MathSciNet review: 2170554
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Abstract | References | Similar Articles | Additional Information

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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