Smoothness criteria for Navier-Stokes equations in terms of regularity along the stream lines
نویسندگان
چکیده
Abstract: This article is devoted to a regularity criteria for solutions of the NavierStokes equations in terms of regularity along the stream lines. More precisely, we prove that if u is a suitable weak solution for the Navier-Stokes equation on [0, T ]×R satisfying the condition that |u·∇F | |u|γ 6 A|F |, in which F = div( u |u| ), A is some given constant, and γ is some positive number with 0 < γ < 1 3 , then it follows that u is smooth over (0, T ) × R.
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