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 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids 35B45 A priori estimates in context of PDEs
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References:

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