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Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. (English) Zbl 1256.35051
Summary: In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, that is, the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions.

MSC:
35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35D35 Strong solutions to PDEs
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