On regularity criteria in terms of pressure for the Navier-Stokes equations in <IMG BORDER="0" SRC="/proc/2006-134-01/S0002-9939-05-08312-7/gif-title0/img1.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On regularity criteria in terms of pressure for the Navier-Stokes equations in

Authors:	Yong Zhou

Institution:	Department of Mathematics, East China Normal University, Shanghai, 200062, People's Republic of China

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).

Keywords:	Navier-Stokes equations regularity criterion integrability of pressure a priori estimates

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