  In this paper, we prove two results about the blow up criterion of the
three-dimensional incompressible Navier-Stokes equation in the sobolev space
$\dot H^{5/2}$. The first one improves the result of \cite{CZ}. The second
deals with the relationship of the blow up in $\dot H^{5/2}$ and some critical
spaces. Fourier analysis and standard techniques are used.

Analysis of PDEs