On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2165-2180.
@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},
     pages = {2165--2180},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.01.008},
     mrnumber = {2569890},
     zbl = {1260.35106},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.008/}
}
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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) no. 6, pp. 2165-2180. doi : 10.1016/j.anihpc.2009.01.008. http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.008/

[1] Beirão Da Veiga H., A New Regularity Class for the Navier-Stokes Equations in R n , Chinese Ann. Math. Ser. B 16 (1995) 407-412. | MR | Zbl

[2] Bony J.-M., 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 | Zbl

[3] Cannone M., Chen Q., Miao C., A Losing Estimate for the Ideal MHD Equations With Application to Blow-Up Criterion, SIAM J. Math. Anal. 38 (2007) 1847-1859. | MR | Zbl

[4] Chen Q., Zhang Z., Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations, Methods Appl. Anal. 13 (2006) 107-122. | MR

[5] Chemin J.-Y., Perfect Incompressible Fluids, Oxford University Press, New York, 1998. | MR | Zbl

[6] Chemin J.-Y., Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, J. Anal. Math. 77 (1999) 27-50. | MR | Zbl

[7] Chemin J.-Y., Lerner N., Flot De Champs De Vecteurs Non Lipschitziens Et Équations De Navier-Stokes, J. Differential Equations 121 (1995) 314-328. | MR | Zbl

[8] Cheskidov A., Shvydkoy R., On the Regularity of Weak Solutions of the 3D Navier-Stokes Equations in B , -1 , arXiv:0708.3067v2[math.AP]. | MR

[9] Danchin R., Estimates in Besov Spaces for Transport and Transport-Diffusion Equations With Almost Lipschitz Coefficients, Rev. Mat. Iberoamericana 21 (2005) 863-888. | MR | Zbl

[10] Danchin R., Paicu M., 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 | Zbl

[11] Escauriaza L., Seregin G., Šverák V., L 3, -Solutions to the Navier-Stokes Equations and Backward Uniqueness, Russian Math. Surveys 58 (2003) 211-250. | MR | Zbl

[12] Gallagher I., Planchon F., On Global Infinite Energy Solutions to the Navier-Stokes Equations in Two Dimensions, Arch. Ration. Mech. Anal. 161 (2002) 307-337. | MR | Zbl

[13] Germain P., Multipliers, Paramultipliers, and Weak-Strong Uniqueness for the Navier-Stokes Equations, J. Differential Equations 226 (2006) 373-428. | MR | Zbl

[14] Giga Y., Solutions for Semilinear Parabolic Equations in L p and Regularity of Weak Solutions of the Navier-Stokes System, J. Differential Equations 62 (1986) 186-212. | MR | Zbl

[15] Kozono H., Sohr H., Remark on Uniqueness of Weak Solutions to the Navier-Stokes Equations, Analysis 16 (1996) 255-271. | MR | Zbl

[16] Kozono H., Taniuchi Y., Bilinear Estimates in BMO and the Navier-Stokes Equations, Math. Z. 235 (2000) 173-194. | MR | Zbl

[17] Kozono H., Ogawa T., Taniuchi Y., The Critical Sobolev Inequalities in Besov Spaces and Regularity Criterion to Some Semi-Linear Evolution Equations, Math. Z. 242 (2002) 251-278. | MR | Zbl

[18] Kozono H., Shimada Y., Bilinear Estimates in Homogeneous Triebel-Lizorkin Spaces and the Navier-Stokes Equations, Math. Nachr. 276 (2004) 63-74. | MR | Zbl

[19] Lemarié-Rieusset P. G., Recent Developments in the Navier-Stokes Problem, Res. Notes Math., vol. 43, Chapman and Hall/CRC, 2002. | MR | Zbl

[20] Lemarié-Rieusset P. G., Uniqueness for the Navier-Stokes Problem: Remarks on a Theorem of Jean-Yves Chemin, Nonlinearity 20 (2007) 1475-1490. | MR | Zbl

[21] Leray J., Sur Le Mouvement D'un Liquids Visqeux Emplissant L'espace, Acta Math. 63 (1934) 193-248. | JFM | MR

[22] Lin F. H., Zhang P., Zhang Z., On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model, Comm. Math. Phys. 277 (2008) 531-553. | MR | Zbl

[23] Majda A. J., Bertozzi A. L., Vorticity and Incompressible Flow, Cambridge University Press, Cambridge, 2002. | MR | Zbl

[24] Masmoudi N., Zhang P., Zhang Z., Global Well-Posedness for 2D Polymeric Fluid Models and Growth Estimate, Physica D 237 (2008) 1663-1675. | MR | Zbl

[25] Prodi G., Un Teorema Di Unicità Per Le Equazioni Di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959) 173-182. | MR | Zbl

[26] Ribaud F., 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 | Zbl

[27] Serrin J., The Initial Value Problem for the Navier-Stokes Equations, in: Langer R. E. (Ed.), Nonlinear Problems, University of Wisconsin Press, Madison, 1963, pp. 69-98. | MR | Zbl

[28] Stein E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. | MR | Zbl

[29] Triebel H., Theory of Function Spaces, Monogr. Math., vol. 78, Birkhäuser-Verlag, Basel, 1983. | MR | Zbl

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