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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 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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