On the blow up criterion of 3D-NSE in Sobolev-Gevrey spaces

TL;DR

This paper improves previous blow-up criteria for 3D Navier-Stokes equations in Sobolev-Gevrey spaces, demonstrating exponential blow-up with less regular initial data using Fourier analysis.

Contribution

It provides a sharper blow-up criterion for 3D Navier-Stokes in Sobolev-Gevrey spaces, reducing initial regularity requirements.

Findings

Establishes exponential blow-up criteria in Sobolev-Gevrey spaces.

Reduces regularity assumptions on initial conditions for blow-up.

Uses Fourier analysis to derive new blow-up results.

Abstract

In \cite{JB1}, Benameur proved a blow-up result of the non regular solution of $(NSE)$ in the Sobolev-Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev-Gevrey spaces with less regularity on the initial condition. Fourier analysis is used.