Electron. J. Diff. Equ., Vol. 2009(2009), No. 121, pp. 1-6.

Two component regularity for the Navier-Stokes equations

Jishan Fan, Hongjun Gao

Abstract:
We consider the regularity of weak solutions to the Navier-Stokes equations in $\mathbb{R}^3$. Let $u:=(u_1,u_2,u_3)$ be a weak solution and $\widetilde{u}:=(u_1,u_2,0)$. We prove that $u$ is strong solution if $\nabla\widetilde{u}$ satisfy Serrin's type criterion.

Submitted August 28, 2009. Published September 29, 2009.
Math Subject Classifications: 35Q30, 35K15, 76D03.
Key Words: Navier-Stokes equations; regularity criterion; two component; multiplier spaces; Besov spaces.

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Jishan Fan
School of Mathematical Science, Nanjing Normal University, Nanjing, 210097, China
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
email: fanjishan@njfu.com.cn
Hongjun Gao
School of Mathematical Science, Nanjing Normal University
Nanjing, 210097, China
email: gaohj@njnu.edu.cn

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