On the blow-up criterion of 3D Navier-Stokes equation in Ḣ5/2

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 (Formula presented.). The first one improves the result of Cortissoz et al. The second deals with the relationship of the blow up in (Formula presented.) and some critical spaces. Fourier analysis and standard techniques are used.