Some remarks on the paper ``On the blow up criterion of 3D Navier-Stokes equations'' by J. Benameur
type: Item
instance of: scholarly article
title: Some remarks on the paper ``On the blow up criterion of 3D Navier-Stokes equations'' by J. Benameur
zbMATH Open document ID: 1307.35188
author: Pablo Braz e Silva
author: Wilberclay G. Melo
author: Paulo R. Zingano
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2014-11-11T00:00:00Z
reviewed by: Il'ya Sh. Mogilevskii
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 6368466
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: blow-up criterion
zbMATH Keywords: Sobolev spaces
MaRDI profile type: Publication
full work available at URL: j.crma.2014.09.012
OpenAlex ID: W2070857932
cites work: Remarks on the breakdown of smooth solutions for the 3-D Euler equations
cites work: On the blow-up criterion of 3D Navier-Stokes equations
cites work: Q3645635
cites work: Q2702181
cites work: Q4075341
cites work: Decay in time of incompressible flows
cites work: Micropolar fluids. Theory and applications
cites work: Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces
cites work: Large-time behaviour of solutions to the magneto-hydrodynamics equations
cites work: Necessary conditions of a potential blow-up for Navier-Stokes equations
cites work: A certain necessary condition of potential blow up for Navier-Stokes equations
cites work: Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations
DOI: 10.1016/J.CRMA.2014.09.012
Recommended article: On the blow-up criterion of 3D Navier-Stokes equations
Recommended article: Blow-up of critical norms for the 3-D Navier-Stokes equations
Recommended article: About some possible blow-up conditions for the 3-D Navier-Stokes equations
Recommended article: REMARKS ON THE BLOW-UP CRITERION FOR THE 3-D BOUSSINESQ EQUATIONS
Recommended article: Remarks on the blow-up criterion of the three-dimensional Euler equations
Recommended article: Some remarks about the possible blow-up for the Navier-Stokes equations
Recommended article: A remark on the blow-up criterion of strong solutions to the Navier-Stokes equations
Recommended article: Q5247711
Recommended article: Remarks on regularity criteria for the 3d Navier-Stokes equations
Recommended article: Some remarks on the Navier–Stokes equations in R3
review text: 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.
description: scientific article; zbMATH DE number 6368466