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In this paper, we prove two results about the blow‐up criterion of the three‐dimensional incompressible Navier‐Stokes equation in the Sobolev spaceH  ̇5  /  2    . The first one improves the result of Cortissoz et al. The second deals with the relationship of the blow up inH  ̇5  /  2and some critical spaces. Fourier analysis and standard techniques are used.

On the blow‐up criterion of 3D Navier‐Stokes equation in H ̇ 5 / 2