On the Blow up criterion of 3D-Navier-Stokes equation in ${\dot{H}}^{5/2}$

Abstract

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.