Some remarks on the paper ``On the blow up criterion of 3D Navier-Stokes equations'' by J. Benameur
The authors give some extensions and generalizations to the results of \textit{J. Benameur} [J. Math. Anal. Appl. 371, No. 2, 719--727 (2010; Zbl 1197.35189)]. The lower bound estimates for the potential blow-up in Sobolev spaces \(H^s\) were established in this paper to the Cauchy problem NEWLINE\[NEWLINE\begin{aligned} \frac{\partial v}{\partial t}+v\cdot\nabla v-\nu\Delta v+\nabla p=0,\quad \text{div}\,v=0,\quad x\in\mathbb{R}^3,\;t>0,\\ v(x,0)=v_0,\quad\text{div}\,v_0=0.\end{aligned}NEWLINE\]NEWLINE J. Benameur obtained blow-up estimates for \(s>5/2\). The authors of the reviewed article establish similar estimates for \(s>1/2\) using minor change in the J. Benameur's proof. They indicate that the J. Benameur's proofs may be sufficiently simplified.
scientific article; zbMATH DE number 6368466
scientific article