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On Regularity Criteria in Terms of Pressure for the Navier-Stokes Equations in R3

Yong Zhou
Proceedings of the American Mathematical Society
Vol. 134, No. 1 (Jan., 2006), pp. 149-156
Stable URL: http://www.jstor.org/stable/4098346
Page Count: 8
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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 R3. 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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