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

TL;DR

This paper investigates conditions under which solutions to the 3D Navier-Stokes equations blow up in the Sobolev space f/2, improving previous criteria and exploring connections with critical spaces using Fourier analysis.

Contribution

It provides improved blow-up criteria in f/2 and examines the relationship between blow-up in this space and other critical function spaces.

Findings

Enhanced blow-up criterion in f/2 space.

Established links between blow-up in f/2 and critical spaces.

Utilized Fourier analysis for the proofs.

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.