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Zbl 1166.35359
Zhou, Yong
A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component.
(English)
[J] Methods Appl. Anal. 9, No. 4, 563-578 (2002). ISSN 1073-2772

Summary: We consider the regularity criteria for the weak solutions to the Navier-Stokes equations in $\bbfR^3$. It is proved that if the gradient of any one component of the velocity field belongs to $L^{\alpha,\gamma}$ with $2/\alpha + 3/\gamma = 3/2$, $3\le\gamma < \infty$, then the weak solution actually is strong.
MSC 2000:
*35Q30 Stokes and Navier-Stokes equations
35B65 Smoothness of solutions of PDE
76D03 Existence, uniqueness, and regularity theory
76D05 Navier-Stokes equations (fluid dynamics)

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