@article{AIHPC_2009__26_6_2165_0,
author = {Chen, Qionglei and Miao, Changxing and Zhang, Zhifei},
title = {On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {26},
year = {2009},
pages = {2165-2180},
doi = {10.1016/j.anihpc.2009.01.008},
mrnumber = {2569890},
zbl = {pre05649868},
zbl = {1260.35106},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2165_0}
}
Chen, Qionglei; Miao, Changxing; Zhang, Zhifei. On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2165-2180. doi : 10.1016/j.anihpc.2009.01.008. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2165_0/
[1] , A New Regularity Class for the Navier-Stokes Equations in , Chinese Ann. Math. Ser. B 16 (1995) 407-412. | MR 1380578 | Zbl 0837.35111
[2] , Calcul Symbolique Et Propagation Des Singularités Pour Les Équations Aux Dérivées Partielles Non Linéaires, Ann. Sci. École Norm. Sup. 14 (1981) 209-246. | Numdam | MR 631751 | Zbl 0495.35024
[3] , , , A Losing Estimate for the Ideal MHD Equations With Application to Blow-Up Criterion, SIAM J. Math. Anal. 38 (2007) 1847-1859. | MR 2299432 | Zbl 1126.76057
[4] , , Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations, Methods Appl. Anal. 13 (2006) 107-122. | MR 2275874 | Zbl pre05123520
[5] , Perfect Incompressible Fluids, Oxford University Press, New York, 1998. | MR 1688875 | Zbl 0927.76002
[6] , Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, J. Anal. Math. 77 (1999) 27-50. | MR 1753481 | Zbl 0938.35125
[7] , , Flot De Champs De Vecteurs Non Lipschitziens Et Équations De Navier-Stokes, J. Differential Equations 121 (1995) 314-328. | MR 1354312 | Zbl 0878.35089
[8] , , On the Regularity of Weak Solutions of the 3D Navier-Stokes Equations in , arXiv:0708.3067v2[math.AP]. | MR 2564471
[9] , Estimates in Besov Spaces for Transport and Transport-Diffusion Equations With Almost Lipschitz Coefficients, Rev. Mat. Iberoamericana 21 (2005) 863-888. | MR 2231013 | Zbl 1098.35038
[10] , , Le Théorème De Leray Et Le Théorème De Fujita-Kato Pour Le Système De Boussinesq Partiellement Visqueux, Bulletin de la Societe Mathematique de France 136 (2008) 261-309. | Numdam | MR 2415344 | Zbl 1162.35063
[11] , , , -Solutions to the Navier-Stokes Equations and Backward Uniqueness, Russian Math. Surveys 58 (2003) 211-250. | MR 1992563 | Zbl 1064.35134
[12] , , On Global Infinite Energy Solutions to the Navier-Stokes Equations in Two Dimensions, Arch. Ration. Mech. Anal. 161 (2002) 307-337. | MR 1891170 | Zbl 1027.35090
[13] , Multipliers, Paramultipliers, and Weak-Strong Uniqueness for the Navier-Stokes Equations, J. Differential Equations 226 (2006) 373-428. | MR 2237686 | Zbl 1104.35033
[14] , Solutions for Semilinear Parabolic Equations in and Regularity of Weak Solutions of the Navier-Stokes System, J. Differential Equations 62 (1986) 186-212. | MR 833416 | Zbl 0577.35058
[15] , , Remark on Uniqueness of Weak Solutions to the Navier-Stokes Equations, Analysis 16 (1996) 255-271. | MR 1403221 | Zbl 0864.35082
[16] , , Bilinear Estimates in BMO and the Navier-Stokes Equations, Math. Z. 235 (2000) 173-194. | MR 1785078 | Zbl 0970.35099
[17] , , , The Critical Sobolev Inequalities in Besov Spaces and Regularity Criterion to Some Semi-Linear Evolution Equations, Math. Z. 242 (2002) 251-278. | MR 1980623 | Zbl 1055.35087
[18] , , Bilinear Estimates in Homogeneous Triebel-Lizorkin Spaces and the Navier-Stokes Equations, Math. Nachr. 276 (2004) 63-74. | MR 2100048 | Zbl 1078.35087
[19] , Recent Developments in the Navier-Stokes Problem, Res. Notes Math., vol. 43, Chapman and Hall/CRC, 2002. | MR 1938147 | Zbl 1034.35093
[20] , Uniqueness for the Navier-Stokes Problem: Remarks on a Theorem of Jean-Yves Chemin, Nonlinearity 20 (2007) 1475-1490. | MR 2327134 | Zbl 1129.35058
[21] , Sur Le Mouvement D'un Liquids Visqeux Emplissant L'espace, Acta Math. 63 (1934) 193-248. | JFM 60.0726.05 | MR 1555394
[22] , , , On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model, Comm. Math. Phys. 277 (2008) 531-553. | MR 2358294 | Zbl 1143.82035
[23] , , Vorticity and Incompressible Flow, Cambridge University Press, Cambridge, 2002. | MR 1867882 | Zbl 0983.76001
[24] , , , Global Well-Posedness for 2D Polymeric Fluid Models and Growth Estimate, Physica D 237 (2008) 1663-1675. | MR 2454611 | Zbl 1143.76356
[25] , Un Teorema Di Unicità Per Le Equazioni Di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959) 173-182. | MR 126088 | Zbl 0148.08202
[26] , A Remark on the Uniqueness Problem for the Weak Solutions of Navier-Stokes Equations, Ann. Fac. Sci. Toulouse Math. 11 (2002) 225-238. | Numdam | MR 1988463 | Zbl 1046.35086
[27] , The Initial Value Problem for the Navier-Stokes Equations, in: (Ed.), Nonlinear Problems, University of Wisconsin Press, Madison, 1963, pp. 69-98. | MR 150444 | Zbl 0115.08502
[28] , Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. | MR 1232192 | Zbl 0821.42001
[29] , Theory of Function Spaces, Monogr. Math., vol. 78, Birkhäuser-Verlag, Basel, 1983. | MR 781540 | Zbl 0546.46027