## On the regularity criteria of the 3D Navier-Stokes equations in critical spaces.(English)Zbl 1240.35382

Summary: Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, $$\partial_1 u_1,\partial_2 u_2$$, of velocity fields.

### MSC:

 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids

### Keywords:

regularity criteria; Navier-Stokes equations
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