Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., 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.

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