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A new regularity criterion for weak solutions to the Navier-Stokes equations. (English) Zbl 1092.35081
A new regularity criterion for weak solutions to the 3D Navier-Stokes equations is obtained. The author shows that if any one component of the velocity field belongs to $L^\alpha ([0,T); L^\gamma (\mathbb{R}^3 ))$ with $\frac{2}{\alpha} + \frac {3} {\gamma} \leq \frac{1}{2}$, $6< \gamma \leq \infty$, then the weak solution actually is regular and unique.

##### MSC:
 35Q30 Stokes and Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory 76D05 Navier-Stokes equations (fluid dynamics) 35B45 A priori estimates for solutions of PDE
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##### References:
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