[Quelques remarques sur l'article « On the blow up criterion of 3D Navier–Stokes equations » par J. Benameur]
Nous indiquons quelques simplifications et extensions importantes des résultats obtenus par J. Benameur concernant des estimations inférieures pour l'explosion des solutions fortes des équations de Navier–Stokes incompressibles dans les espaces de Sobolev homogènes , , en cas d'existence non globale.
We indicate some important simplifications and extensions of the analysis recently given by J. Benameur to derive blow-up estimates for strong solutions to 3D incompressible Navier–Stokes equations in homogeneous Sobolev spaces , , in case of finite-time existence.
Accepté le :
Publié le :
@article{CRMATH_2014__352_11_913_0,
author = {Pablo Braz e Silva and Wilberclay G. Melo and Paulo R. Zingano},
title = {Some remarks on the paper {{\textquotedblleft}On} the blow up criterion of {3D} {Navier{\textendash}Stokes} equations{\textquotedblright} by {J.} {Benameur}},
journal = {Comptes Rendus. Math\'ematique},
pages = {913--915},
publisher = {Elsevier},
volume = {352},
number = {11},
year = {2014},
doi = {10.1016/j.crma.2014.09.012},
language = {en},
}
TY - JOUR AU - Pablo Braz e Silva AU - Wilberclay G. Melo AU - Paulo R. Zingano TI - Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur JO - Comptes Rendus. Mathématique PY - 2014 SP - 913 EP - 915 VL - 352 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2014.09.012 LA - en ID - CRMATH_2014__352_11_913_0 ER -
%0 Journal Article %A Pablo Braz e Silva %A Wilberclay G. Melo %A Paulo R. Zingano %T Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur %J Comptes Rendus. Mathématique %D 2014 %P 913-915 %V 352 %N 11 %I Elsevier %R 10.1016/j.crma.2014.09.012 %G en %F CRMATH_2014__352_11_913_0
Pablo Braz e Silva; Wilberclay G. Melo; Paulo R. Zingano. Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 913-915. doi : 10.1016/j.crma.2014.09.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.012/
[1] Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun. Math. Phys., Volume 94 (1984), pp. 61-66
[2] On the blow-up criterion of 3D Navier–Stokes equations, J. Math. Anal. Appl., Volume 371 (2010), pp. 719-727
[3] Incompressible Euler equations: the blow–up problem and related results (C.M. Dafermos; M. Pokorny, eds.), Handbook of Differential Equations: Evolutionary Equations, vol. IV, Elsevier, Amsterdam, 2008, pp. 1-55
[4] An introduction to the Navier–Stokes initial-boundary problem (G.P. Galdi; J.G. Heywood; R. Rannacher, eds.), Fundamental Directions in Mathematical Fluid Dynamics, Birkhauser, Basel, Switzerland, 2000, pp. 1-70
[5] Quasilinear equations of evolution, with applications to partial differential equations, 1974 (Lect. Notes Math.), Volume vol. 448 (1975)
[6] Decay in time of incompressible flows, J. Math. Fluid Mech., Volume 5 (2003), pp. 231-244
[7] Essai sur le mouvement d'un fluide visqueux emplissant l'espace, Acta Math., Volume 63 (1934), pp. 193-248
[8] Microloplar Fluids: Theory and Applications, Birkhäuser, Berlin, 1999
[9] Lower bounds on blow-up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces, J. Math. Phys., Volume 53 (2012)
[10] Large-time behaviour of the magnetohydrodynamics equations, Math. Ann., Volume 304 (1996), pp. 717-756
[11] Necessary conditions of potential blow-up for the Navier–Stokes equations, J. Math. Sci., Volume 178 (2011), pp. 345-352
[12] A certain necessary condition of potential blow-up for Navier–Stokes equations, Commun. Math. Phys., Volume 312 (2012), pp. 833-845
[13] Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations, Math. Methods Appl. Sci., Volume 31 (2008), pp. 1113-1130
Cité par Sources :
Commentaires - Politique