Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor Academic Article uri icon


  • 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. © 2011 Springer-Verlag.

author list (cited authors)

  • Cao, C., & Titi, E. S.

citation count

  • 120

publication date

  • July 2011